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Mathematical equation/notation
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1
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favorite
How do I represent the following sum of products using summation notation?
$$P = p_1 q_1 + p_2 (q_1+q_2) + p_3(q_1+q_2+q_3) + dots $$
Here is my attempt:
$P$ = $sum_i=1^np_isum_i=1^iq_i$
where $i = 1,2,...n$
Thanks
Note: what I am trying to capture in my equation is the sum of the product of a function 1 (p) with the cumulative sum of function 2(q) such that they both have the same number of elements
index-notation
edited Jul 25 at 23:10
ComplexYetTrivial
2,827624
asked Jul 25 at 23:04
hkf
1083
add a comment |Â
up vote
1
down vote
favorite
How do I represent the following sum of products using summation notation?
$$P = p_1 q_1 + p_2 (q_1+q_2) + p_3(q_1+q_2+q_3) + dots $$
Here is my attempt:
$P$ = $sum_i=1^np_isum_i=1^iq_i$
where $i = 1,2,...n$
Thanks
Note: what I am trying to capture in my equation is the sum of the product of a function 1 (p) with the cumulative sum of function 2(q) such that they both have the same number of elements
index-notation
edited Jul 25 at 23:10
ComplexYetTrivial
2,827624
asked Jul 25 at 23:04
hkf
1083
1
$sum_i=1^i$ is confusing. The $i$ in the bottom is the summation variable, while the $i$ on top is an actual parameter. They should have different names: $sum_i=1^nleft(p_isum_j=1^iq_jright)$.
– user578878
Jul 25 at 23:08
is there an alternate notation where introducing another parameter "j" can be avoided?
– hkf
Jul 25 at 23:11
2
Determining the correctness of a proof or expression that reuses names to denote different things becomes very complicated very easily. That is a problem both for the writer and for the reader. You want to be understood and the correctness of your arguments to be easy to determine. That is why it should be avoided as much as possible, and some people opt to even prohibit it.
– user578878
Jul 25 at 23:15
1
If you are a computer executing that formula and are given the value $i=3$ for the upper limit of the summation. Then to compute what to sum, you need to put $i=1$ as the first index and compute $q_1$. If you or someone reading interprets both $i$'s as the same storage unit (after all it is the same name), then the stopping condition for the summation would be $i>i$. Since this condition doesn't get satisfied, the summation never stops adding, while it was intended to have only $3$ terms.
– user578878
Jul 25 at 23:28
... or not run at all, if the stopping condition is checked before starting to add or if it is $ileq i$.
– user578878
Jul 25 at 23:34
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
How do I represent the following sum of products using summation notation?
$$P = p_1 q_1 + p_2 (q_1+q_2) + p_3(q_1+q_2+q_3) + dots $$
Here is my attempt:
$P$ = $sum_i=1^np_isum_i=1^iq_i$
where $i = 1,2,...n$
Thanks
Note: what I am trying to capture in my equation is the sum of the product of a function 1 (p) with the cumulative sum of function 2(q) such that they both have the same number of elements
index-notation
edited Jul 25 at 23:10
ComplexYetTrivial
2,827624
asked Jul 25 at 23:04
hkf
1083
How do I represent the following sum of products using summation notation?
$$P = p_1 q_1 + p_2 (q_1+q_2) + p_3(q_1+q_2+q_3) + dots $$
Here is my attempt:
$P$ = $sum_i=1^np_isum_i=1^iq_i$
where $i = 1,2,...n$
Thanks
Note: what I am trying to capture in my equation is the sum of the product of a function 1 (p) with the cumulative sum of function 2(q) such that they both have the same number of elements
index-notation
edited Jul 25 at 23:10
ComplexYetTrivial
2,827624
asked Jul 25 at 23:04
hkf
1083
edited Jul 25 at 23:10
ComplexYetTrivial
2,827624
edited Jul 25 at 23:10
ComplexYetTrivial
2,827624
edited Jul 25 at 23:10
ComplexYetTrivial
2,827624
2,827624
asked Jul 25 at 23:04
hkf
1083
asked Jul 25 at 23:04
hkf
1083
asked Jul 25 at 23:04
hkf
1083
1083
1
$sum_i=1^i$ is confusing. The $i$ in the bottom is the summation variable, while the $i$ on top is an actual parameter. They should have different names: $sum_i=1^nleft(p_isum_j=1^iq_jright)$.
– user578878
Jul 25 at 23:08
is there an alternate notation where introducing another parameter "j" can be avoided?
– hkf
Jul 25 at 23:11
2
Determining the correctness of a proof or expression that reuses names to denote different things becomes very complicated very easily. That is a problem both for the writer and for the reader. You want to be understood and the correctness of your arguments to be easy to determine. That is why it should be avoided as much as possible, and some people opt to even prohibit it.
– user578878
Jul 25 at 23:15
1
If you are a computer executing that formula and are given the value $i=3$ for the upper limit of the summation. Then to compute what to sum, you need to put $i=1$ as the first index and compute $q_1$. If you or someone reading interprets both $i$'s as the same storage unit (after all it is the same name), then the stopping condition for the summation would be $i>i$. Since this condition doesn't get satisfied, the summation never stops adding, while it was intended to have only $3$ terms.
– user578878
Jul 25 at 23:28
... or not run at all, if the stopping condition is checked before starting to add or if it is $ileq i$.
– user578878
Jul 25 at 23:34
add a comment |Â
1
$sum_i=1^i$ is confusing. The $i$ in the bottom is the summation variable, while the $i$ on top is an actual parameter. They should have different names: $sum_i=1^nleft(p_isum_j=1^iq_jright)$.
– user578878
Jul 25 at 23:08
is there an alternate notation where introducing another parameter "j" can be avoided?
– hkf
Jul 25 at 23:11
2
Determining the correctness of a proof or expression that reuses names to denote different things becomes very complicated very easily. That is a problem both for the writer and for the reader. You want to be understood and the correctness of your arguments to be easy to determine. That is why it should be avoided as much as possible, and some people opt to even prohibit it.
– user578878
Jul 25 at 23:15
1
If you are a computer executing that formula and are given the value $i=3$ for the upper limit of the summation. Then to compute what to sum, you need to put $i=1$ as the first index and compute $q_1$. If you or someone reading interprets both $i$'s as the same storage unit (after all it is the same name), then the stopping condition for the summation would be $i>i$. Since this condition doesn't get satisfied, the summation never stops adding, while it was intended to have only $3$ terms.
– user578878
Jul 25 at 23:28
... or not run at all, if the stopping condition is checked before starting to add or if it is $ileq i$.
– user578878
Jul 25 at 23:34
1
1
$sum_i=1^i$ is confusing. The $i$ in the bottom is the summation variable, while the $i$ on top is an actual parameter. They should have different names: $sum_i=1^nleft(p_isum_j=1^iq_jright)$.
– user578878
Jul 25 at 23:08
$sum_i=1^i$ is confusing. The $i$ in the bottom is the summation variable, while the $i$ on top is an actual parameter. They should have different names: $sum_i=1^nleft(p_isum_j=1^iq_jright)$.
– user578878
Jul 25 at 23:08
is there an alternate notation where introducing another parameter "j" can be avoided?
– hkf
Jul 25 at 23:11
is there an alternate notation where introducing another parameter "j" can be avoided?
– hkf
Jul 25 at 23:11
2
2
Determining the correctness of a proof or expression that reuses names to denote different things becomes very complicated very easily. That is a problem both for the writer and for the reader. You want to be understood and the correctness of your arguments to be easy to determine. That is why it should be avoided as much as possible, and some people opt to even prohibit it.
– user578878
Jul 25 at 23:15
Determining the correctness of a proof or expression that reuses names to denote different things becomes very complicated very easily. That is a problem both for the writer and for the reader. You want to be understood and the correctness of your arguments to be easy to determine. That is why it should be avoided as much as possible, and some people opt to even prohibit it.
– user578878
Jul 25 at 23:15
1
1
If you are a computer executing that formula and are given the value $i=3$ for the upper limit of the summation. Then to compute what to sum, you need to put $i=1$ as the first index and compute $q_1$. If you or someone reading interprets both $i$'s as the same storage unit (after all it is the same name), then the stopping condition for the summation would be $i>i$. Since this condition doesn't get satisfied, the summation never stops adding, while it was intended to have only $3$ terms.
– user578878
Jul 25 at 23:28
If you are a computer executing that formula and are given the value $i=3$ for the upper limit of the summation. Then to compute what to sum, you need to put $i=1$ as the first index and compute $q_1$. If you or someone reading interprets both $i$'s as the same storage unit (after all it is the same name), then the stopping condition for the summation would be $i>i$. Since this condition doesn't get satisfied, the summation never stops adding, while it was intended to have only $3$ terms.
– user578878
Jul 25 at 23:28
... or not run at all, if the stopping condition is checked before starting to add or if it is $ileq i$.
– user578878
Jul 25 at 23:34
... or not run at all, if the stopping condition is checked before starting to add or if it is $ileq i$.
– user578878
Jul 25 at 23:34
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
3
down vote
accepted
I would write it $$sum_i=1^nleft(p_isum_k=1^i q_kright)$$
which is the same as
$$sum_i=1^nleft(sum_k=1^i p_iq_kright)$$
Or again (after inverting the two sum symbols)
$$sum_k=1^nleft(sum_i=k^n p_iq_kright)$$
Note that you can not use the same summation index for two separate sums, it makes no sense. I chose the letter $k$ for the second sum, but you can use just any letter you would like (except $i$, $n$, and also $p$, $q$).
answered Jul 25 at 23:10
Suzet
2,213427
2
Why only letters? $sum_clubsuit=1^n p_clubsuit sum_diamondsuit=1^clubsuit q_diamondsuit$ is a favorite of mine.
– Clement C.
Jul 25 at 23:17
1
$sum_数=1^nleft(p_数sum_å¦=1^数 q_å¦right)$ (just testing if this worked)
– Suzet
Jul 25 at 23:20
@Suzet: Now you're just getting silly. Everyone knows that summation indices should use traditional characters.
– Brian Tung
Jul 25 at 23:42
@BrianTung Oh right, silly me. Actually, I meant $sum_䨺=1^nleft(p_䨺sum_龘=1^䨺 q_龘right)$
– Suzet
Jul 26 at 0:59
@Suzet: Hahaha. Even at maximum zoom that doesn't show clearly. (I know those famous characters, but still!)
– Brian Tung
Jul 26 at 4:52
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
I would write it $$sum_i=1^nleft(p_isum_k=1^i q_kright)$$
which is the same as
$$sum_i=1^nleft(sum_k=1^i p_iq_kright)$$
Or again (after inverting the two sum symbols)
$$sum_k=1^nleft(sum_i=k^n p_iq_kright)$$
Note that you can not use the same summation index for two separate sums, it makes no sense. I chose the letter $k$ for the second sum, but you can use just any letter you would like (except $i$, $n$, and also $p$, $q$).
answered Jul 25 at 23:10
Suzet
2,213427
2
Why only letters? $sum_clubsuit=1^n p_clubsuit sum_diamondsuit=1^clubsuit q_diamondsuit$ is a favorite of mine.
– Clement C.
Jul 25 at 23:17
1
$sum_数=1^nleft(p_数sum_å¦=1^数 q_å¦right)$ (just testing if this worked)
– Suzet
Jul 25 at 23:20
@Suzet: Now you're just getting silly. Everyone knows that summation indices should use traditional characters.
– Brian Tung
Jul 25 at 23:42
@BrianTung Oh right, silly me. Actually, I meant $sum_䨺=1^nleft(p_䨺sum_龘=1^䨺 q_龘right)$
– Suzet
Jul 26 at 0:59
@Suzet: Hahaha. Even at maximum zoom that doesn't show clearly. (I know those famous characters, but still!)
– Brian Tung
Jul 26 at 4:52
add a comment |Â
up vote
3
down vote
accepted
I would write it $$sum_i=1^nleft(p_isum_k=1^i q_kright)$$
which is the same as
$$sum_i=1^nleft(sum_k=1^i p_iq_kright)$$
Or again (after inverting the two sum symbols)
$$sum_k=1^nleft(sum_i=k^n p_iq_kright)$$
Note that you can not use the same summation index for two separate sums, it makes no sense. I chose the letter $k$ for the second sum, but you can use just any letter you would like (except $i$, $n$, and also $p$, $q$).
answered Jul 25 at 23:10
Suzet
2,213427
2
Why only letters? $sum_clubsuit=1^n p_clubsuit sum_diamondsuit=1^clubsuit q_diamondsuit$ is a favorite of mine.
– Clement C.
Jul 25 at 23:17
1
$sum_数=1^nleft(p_数sum_å¦=1^数 q_å¦right)$ (just testing if this worked)
– Suzet
Jul 25 at 23:20
@Suzet: Now you're just getting silly. Everyone knows that summation indices should use traditional characters.
– Brian Tung
Jul 25 at 23:42
@BrianTung Oh right, silly me. Actually, I meant $sum_䨺=1^nleft(p_䨺sum_龘=1^䨺 q_龘right)$
– Suzet
Jul 26 at 0:59
@Suzet: Hahaha. Even at maximum zoom that doesn't show clearly. (I know those famous characters, but still!)
– Brian Tung
Jul 26 at 4:52
add a comment |Â
up vote
3
down vote
accepted
up vote
3
down vote
accepted
I would write it $$sum_i=1^nleft(p_isum_k=1^i q_kright)$$
which is the same as
$$sum_i=1^nleft(sum_k=1^i p_iq_kright)$$
Or again (after inverting the two sum symbols)
$$sum_k=1^nleft(sum_i=k^n p_iq_kright)$$
Note that you can not use the same summation index for two separate sums, it makes no sense. I chose the letter $k$ for the second sum, but you can use just any letter you would like (except $i$, $n$, and also $p$, $q$).
answered Jul 25 at 23:10
Suzet
2,213427
I would write it $$sum_i=1^nleft(p_isum_k=1^i q_kright)$$
which is the same as
$$sum_i=1^nleft(sum_k=1^i p_iq_kright)$$
Or again (after inverting the two sum symbols)
$$sum_k=1^nleft(sum_i=k^n p_iq_kright)$$
Note that you can not use the same summation index for two separate sums, it makes no sense. I chose the letter $k$ for the second sum, but you can use just any letter you would like (except $i$, $n$, and also $p$, $q$).
answered Jul 25 at 23:10
Suzet
2,213427
answered Jul 25 at 23:10
Suzet
2,213427
answered Jul 25 at 23:10
Suzet
2,213427
answered Jul 25 at 23:10
Suzet
2,213427
2,213427
2
Why only letters? $sum_clubsuit=1^n p_clubsuit sum_diamondsuit=1^clubsuit q_diamondsuit$ is a favorite of mine.
– Clement C.
Jul 25 at 23:17
1
$sum_数=1^nleft(p_数sum_å¦=1^数 q_å¦right)$ (just testing if this worked)
– Suzet
Jul 25 at 23:20
@Suzet: Now you're just getting silly. Everyone knows that summation indices should use traditional characters.
– Brian Tung
Jul 25 at 23:42
@BrianTung Oh right, silly me. Actually, I meant $sum_䨺=1^nleft(p_䨺sum_龘=1^䨺 q_龘right)$
– Suzet
Jul 26 at 0:59
@Suzet: Hahaha. Even at maximum zoom that doesn't show clearly. (I know those famous characters, but still!)
– Brian Tung
Jul 26 at 4:52
add a comment |Â
2
Why only letters? $sum_clubsuit=1^n p_clubsuit sum_diamondsuit=1^clubsuit q_diamondsuit$ is a favorite of mine.
– Clement C.
Jul 25 at 23:17
1
$sum_数=1^nleft(p_数sum_å¦=1^数 q_å¦right)$ (just testing if this worked)
– Suzet
Jul 25 at 23:20
@Suzet: Now you're just getting silly. Everyone knows that summation indices should use traditional characters.
– Brian Tung
Jul 25 at 23:42
@BrianTung Oh right, silly me. Actually, I meant $sum_䨺=1^nleft(p_䨺sum_龘=1^䨺 q_龘right)$
– Suzet
Jul 26 at 0:59
@Suzet: Hahaha. Even at maximum zoom that doesn't show clearly. (I know those famous characters, but still!)
– Brian Tung
Jul 26 at 4:52
2
2
Why only letters? $sum_clubsuit=1^n p_clubsuit sum_diamondsuit=1^clubsuit q_diamondsuit$ is a favorite of mine.
– Clement C.
Jul 25 at 23:17
Why only letters? $sum_clubsuit=1^n p_clubsuit sum_diamondsuit=1^clubsuit q_diamondsuit$ is a favorite of mine.
– Clement C.
Jul 25 at 23:17
1
1
$sum_数=1^nleft(p_数sum_å¦=1^数 q_å¦right)$ (just testing if this worked)
– Suzet
Jul 25 at 23:20
$sum_数=1^nleft(p_数sum_å¦=1^数 q_å¦right)$ (just testing if this worked)
– Suzet
Jul 25 at 23:20
@Suzet: Now you're just getting silly. Everyone knows that summation indices should use traditional characters.
– Brian Tung
Jul 25 at 23:42
@Suzet: Now you're just getting silly. Everyone knows that summation indices should use traditional characters.
– Brian Tung
Jul 25 at 23:42
@BrianTung Oh right, silly me. Actually, I meant $sum_䨺=1^nleft(p_䨺sum_龘=1^䨺 q_龘right)$
– Suzet
Jul 26 at 0:59
@BrianTung Oh right, silly me. Actually, I meant $sum_䨺=1^nleft(p_䨺sum_龘=1^䨺 q_龘right)$
– Suzet
Jul 26 at 0:59
@Suzet: Hahaha. Even at maximum zoom that doesn't show clearly. (I know those famous characters, but still!)
– Brian Tung
Jul 26 at 4:52
@Suzet: Hahaha. Even at maximum zoom that doesn't show clearly. (I know those famous characters, but still!)
– Brian Tung
Jul 26 at 4:52
add a comment |Â
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1
$sum_i=1^i$ is confusing. The $i$ in the bottom is the summation variable, while the $i$ on top is an actual parameter. They should have different names: $sum_i=1^nleft(p_isum_j=1^iq_jright)$.
– user578878
Jul 25 at 23:08
is there an alternate notation where introducing another parameter "j" can be avoided?
– hkf
Jul 25 at 23:11
2
Determining the correctness of a proof or expression that reuses names to denote different things becomes very complicated very easily. That is a problem both for the writer and for the reader. You want to be understood and the correctness of your arguments to be easy to determine. That is why it should be avoided as much as possible, and some people opt to even prohibit it.
– user578878
Jul 25 at 23:15
1
If you are a computer executing that formula and are given the value $i=3$ for the upper limit of the summation. Then to compute what to sum, you need to put $i=1$ as the first index and compute $q_1$. If you or someone reading interprets both $i$'s as the same storage unit (after all it is the same name), then the stopping condition for the summation would be $i>i$. Since this condition doesn't get satisfied, the summation never stops adding, while it was intended to have only $3$ terms.
– user578878
Jul 25 at 23:28
... or not run at all, if the stopping condition is checked before starting to add or if it is $ileq i$.
– user578878
Jul 25 at 23:34