Don’t understand solution to nested sums [on hold]

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Solution to a problem I was working on

While checking my answers, I came across this solution. I don’t understand why you need to subtract the sum of the first i-1 integers and I don’t understand why the second sum is 7(13-i) and not 84. Could someone please explain it to me?

sequences-and-series

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asked Aug 2 at 18:16

Alex Ruan

1

put on hold as off-topic by John Ma, Isaac Browne, Taroccoesbrocco, Shailesh, Xander Henderson Aug 3 at 2:02

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – John Ma, Isaac Browne, Taroccoesbrocco, Shailesh, Xander Henderson

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Hi @Alex, welcome to math.stackexchange. If you could write out your problem in text rather than linking to an image, it would help a lot. Otherwise other users can't search the site for your question, or the image's URL may cease to work at some point.
  – Jam
  Aug 2 at 18:31
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @Jam More importantly, it's more annoying to read...
  – Jack M
  Aug 2 at 18:37
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @JackM Yeah that's the main reason, I'll be honest
  – Jam
  Aug 2 at 18:38
  

  
  
  
  

add a comment | 

up vote
-5
down vote

favorite

1

Solution to a problem I was working on

While checking my answers, I came across this solution. I don’t understand why you need to subtract the sum of the first i-1 integers and I don’t understand why the second sum is 7(13-i) and not 84. Could someone please explain it to me?

sequences-and-series

share|cite|improve this question

asked Aug 2 at 18:16

Alex Ruan

1

put on hold as off-topic by John Ma, Isaac Browne, Taroccoesbrocco, Shailesh, Xander Henderson Aug 3 at 2:02

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – John Ma, Isaac Browne, Taroccoesbrocco, Shailesh, Xander Henderson

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Hi @Alex, welcome to math.stackexchange. If you could write out your problem in text rather than linking to an image, it would help a lot. Otherwise other users can't search the site for your question, or the image's URL may cease to work at some point.
  – Jam
  Aug 2 at 18:31
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @Jam More importantly, it's more annoying to read...
  – Jack M
  Aug 2 at 18:37
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @JackM Yeah that's the main reason, I'll be honest
  – Jam
  Aug 2 at 18:38
  

  
  
  
  

add a comment | 

up vote
-5
down vote

favorite

1

up vote
-5
down vote

favorite

1

1

Solution to a problem I was working on

While checking my answers, I came across this solution. I don’t understand why you need to subtract the sum of the first i-1 integers and I don’t understand why the second sum is 7(13-i) and not 84. Could someone please explain it to me?

sequences-and-series

share|cite|improve this question

asked Aug 2 at 18:16

Alex Ruan

1

Solution to a problem I was working on

While checking my answers, I came across this solution. I don’t understand why you need to subtract the sum of the first i-1 integers and I don’t understand why the second sum is 7(13-i) and not 84. Could someone please explain it to me?

sequences-and-series

share|cite|improve this question

asked Aug 2 at 18:16

Alex Ruan

1

share|cite|improve this question

share|cite|improve this question

asked Aug 2 at 18:16

Alex Ruan

1

asked Aug 2 at 18:16

Alex Ruan

1

asked Aug 2 at 18:16

Alex Ruan

1

1

put on hold as off-topic by John Ma, Isaac Browne, Taroccoesbrocco, Shailesh, Xander Henderson Aug 3 at 2:02

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – John Ma, Isaac Browne, Taroccoesbrocco, Shailesh, Xander Henderson

If this question can be reworded to fit the rules in the help center, please edit the question.

put on hold as off-topic by John Ma, Isaac Browne, Taroccoesbrocco, Shailesh, Xander Henderson Aug 3 at 2:02

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – John Ma, Isaac Browne, Taroccoesbrocco, Shailesh, Xander Henderson

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Hi @Alex, welcome to math.stackexchange. If you could write out your problem in text rather than linking to an image, it would help a lot. Otherwise other users can't search the site for your question, or the image's URL may cease to work at some point.
  – Jam
  Aug 2 at 18:31
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @Jam More importantly, it's more annoying to read...
  – Jack M
  Aug 2 at 18:37
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @JackM Yeah that's the main reason, I'll be honest
  – Jam
  Aug 2 at 18:38
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Hi @Alex, welcome to math.stackexchange. If you could write out your problem in text rather than linking to an image, it would help a lot. Otherwise other users can't search the site for your question, or the image's URL may cease to work at some point.
  – Jam
  Aug 2 at 18:31
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @Jam More importantly, it's more annoying to read...
  – Jack M
  Aug 2 at 18:37
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @JackM Yeah that's the main reason, I'll be honest
  – Jam
  Aug 2 at 18:38
  

  
  
  
  

1

1

Hi @Alex, welcome to math.stackexchange. If you could write out your problem in text rather than linking to an image, it would help a lot. Otherwise other users can't search the site for your question, or the image's URL may cease to work at some point.
– Jam
Aug 2 at 18:31

Hi @Alex, welcome to math.stackexchange. If you could write out your problem in text rather than linking to an image, it would help a lot. Otherwise other users can't search the site for your question, or the image's URL may cease to work at some point.
– Jam
Aug 2 at 18:31

1

1

@Jam More importantly, it's more annoying to read...
– Jack M
Aug 2 at 18:37

@Jam More importantly, it's more annoying to read...
– Jack M
Aug 2 at 18:37

1

1

@JackM Yeah that's the main reason, I'll be honest
– Jam
Aug 2 at 18:38

@JackM Yeah that's the main reason, I'll be honest
– Jam
Aug 2 at 18:38

add a comment | 

1 Answer
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These sums are not from $1$ to $12$ as you seem to think, they're from $i$ to $12$, where $i$ is some number less than $12$. So if say $i$ were $10$, that first sum would be

$$sum^12_j=10(2j-7)=(2cdot10 - 7)+(2cdot11 - 7)+(2cdot12 - 7)$$

share|cite|improve this answer

answered Aug 2 at 18:27

Jack M

16.9k33473

add a comment | 

1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
1
down vote

These sums are not from $1$ to $12$ as you seem to think, they're from $i$ to $12$, where $i$ is some number less than $12$. So if say $i$ were $10$, that first sum would be

$$sum^12_j=10(2j-7)=(2cdot10 - 7)+(2cdot11 - 7)+(2cdot12 - 7)$$

share|cite|improve this answer

answered Aug 2 at 18:27

Jack M

16.9k33473

add a comment | 

up vote
1
down vote

These sums are not from $1$ to $12$ as you seem to think, they're from $i$ to $12$, where $i$ is some number less than $12$. So if say $i$ were $10$, that first sum would be

$$sum^12_j=10(2j-7)=(2cdot10 - 7)+(2cdot11 - 7)+(2cdot12 - 7)$$

share|cite|improve this answer

answered Aug 2 at 18:27

Jack M

16.9k33473

add a comment | 

up vote
1
down vote

up vote
1
down vote

These sums are not from $1$ to $12$ as you seem to think, they're from $i$ to $12$, where $i$ is some number less than $12$. So if say $i$ were $10$, that first sum would be

$$sum^12_j=10(2j-7)=(2cdot10 - 7)+(2cdot11 - 7)+(2cdot12 - 7)$$

share|cite|improve this answer

answered Aug 2 at 18:27

Jack M

16.9k33473

These sums are not from $1$ to $12$ as you seem to think, they're from $i$ to $12$, where $i$ is some number less than $12$. So if say $i$ were $10$, that first sum would be

$$sum^12_j=10(2j-7)=(2cdot10 - 7)+(2cdot11 - 7)+(2cdot12 - 7)$$

share|cite|improve this answer

answered Aug 2 at 18:27

Jack M

16.9k33473

share|cite|improve this answer

share|cite|improve this answer

answered Aug 2 at 18:27

Jack M

16.9k33473

answered Aug 2 at 18:27

Jack M

16.9k33473

answered Aug 2 at 18:27

Jack M

16.9k33473

16.9k33473

add a comment | 

add a comment |