Please simplify this sigma question? [closed]

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I am not able to solve this sigma question. Please anybody solve this question by steps.
$$sum_R=1^Nleft(frac13right)^R-1$$

summation

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edited Jul 18 at 6:01

Parcly Taxel

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asked Jul 18 at 5:58

Rafael Nadal

1076

closed as off-topic by Alex Francisco, TheGeekGreek, José Carlos Santos, Claude Leibovici, Gibbs Jul 18 at 9:16

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." – Alex Francisco, TheGeekGreek, José Carlos Santos, Claude Leibovici, Gibbs

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

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  That's a geometric progression. Bad luck at Wimbledon!
  – Lord Shark the Unknown
  Jul 18 at 6:00
  

  
  
  
  

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up vote
-2
down vote

favorite

I am not able to solve this sigma question. Please anybody solve this question by steps.
$$sum_R=1^Nleft(frac13right)^R-1$$

summation

share|cite|improve this question

edited Jul 18 at 6:01

Parcly Taxel

33.6k136588

asked Jul 18 at 5:58

Rafael Nadal

1076

closed as off-topic by Alex Francisco, TheGeekGreek, José Carlos Santos, Claude Leibovici, Gibbs Jul 18 at 9:16

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." – Alex Francisco, TheGeekGreek, José Carlos Santos, Claude Leibovici, Gibbs

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

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  That's a geometric progression. Bad luck at Wimbledon!
  – Lord Shark the Unknown
  Jul 18 at 6:00
  

  
  
  
  

add a comment | 

up vote
-2
down vote

favorite

up vote
-2
down vote

favorite

I am not able to solve this sigma question. Please anybody solve this question by steps.
$$sum_R=1^Nleft(frac13right)^R-1$$

summation

share|cite|improve this question

edited Jul 18 at 6:01

Parcly Taxel

33.6k136588

asked Jul 18 at 5:58

Rafael Nadal

1076

I am not able to solve this sigma question. Please anybody solve this question by steps.
$$sum_R=1^Nleft(frac13right)^R-1$$

summation

share|cite|improve this question

edited Jul 18 at 6:01

Parcly Taxel

33.6k136588

asked Jul 18 at 5:58

Rafael Nadal

1076

share|cite|improve this question

share|cite|improve this question

edited Jul 18 at 6:01

Parcly Taxel

33.6k136588

edited Jul 18 at 6:01

Parcly Taxel

33.6k136588

edited Jul 18 at 6:01

Parcly Taxel

33.6k136588

33.6k136588

asked Jul 18 at 5:58

Rafael Nadal

1076

asked Jul 18 at 5:58

Rafael Nadal

1076

asked Jul 18 at 5:58

Rafael Nadal

1076

1076

closed as off-topic by Alex Francisco, TheGeekGreek, José Carlos Santos, Claude Leibovici, Gibbs Jul 18 at 9:16

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." – Alex Francisco, TheGeekGreek, José Carlos Santos, Claude Leibovici, Gibbs

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

closed as off-topic by Alex Francisco, TheGeekGreek, José Carlos Santos, Claude Leibovici, Gibbs Jul 18 at 9:16

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." – Alex Francisco, TheGeekGreek, José Carlos Santos, Claude Leibovici, Gibbs

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

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  That's a geometric progression. Bad luck at Wimbledon!
  – Lord Shark the Unknown
  Jul 18 at 6:00
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  That's a geometric progression. Bad luck at Wimbledon!
  – Lord Shark the Unknown
  Jul 18 at 6:00
  

  
  
  
  

3

3

That's a geometric progression. Bad luck at Wimbledon!
– Lord Shark the Unknown
Jul 18 at 6:00

That's a geometric progression. Bad luck at Wimbledon!
– Lord Shark the Unknown
Jul 18 at 6:00

add a comment | 

1 Answer
1

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2
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accepted

Let $r=frac13$, and
$$S_N=sum_R=1^Nleft(frac13right)^R-1=sum_R=1^Nr^R-1$$

You have
$$rS_N=rsum_R=1^Nr^R-1=sum_R=1^Nr^R$$
Then
$$S(r-1)=rS-S=sum_R=1^Nr^R-sum_R=1^Nr^R-1=cdots=r^N-r^0$$
So
$$S=dfrac1-r^N1-r=frac32left(1-frac13^Nright)$$

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answered Jul 18 at 6:17

Karn Watcharasupat

3,8192426

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1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
2
down vote



accepted

Let $r=frac13$, and
$$S_N=sum_R=1^Nleft(frac13right)^R-1=sum_R=1^Nr^R-1$$

You have
$$rS_N=rsum_R=1^Nr^R-1=sum_R=1^Nr^R$$
Then
$$S(r-1)=rS-S=sum_R=1^Nr^R-sum_R=1^Nr^R-1=cdots=r^N-r^0$$
So
$$S=dfrac1-r^N1-r=frac32left(1-frac13^Nright)$$

share|cite|improve this answer

answered Jul 18 at 6:17

Karn Watcharasupat

3,8192426

add a comment | 

up vote
2
down vote



accepted

Let $r=frac13$, and
$$S_N=sum_R=1^Nleft(frac13right)^R-1=sum_R=1^Nr^R-1$$

You have
$$rS_N=rsum_R=1^Nr^R-1=sum_R=1^Nr^R$$
Then
$$S(r-1)=rS-S=sum_R=1^Nr^R-sum_R=1^Nr^R-1=cdots=r^N-r^0$$
So
$$S=dfrac1-r^N1-r=frac32left(1-frac13^Nright)$$

share|cite|improve this answer

answered Jul 18 at 6:17

Karn Watcharasupat

3,8192426

add a comment | 

up vote
2
down vote



accepted

up vote
2
down vote



accepted

Let $r=frac13$, and
$$S_N=sum_R=1^Nleft(frac13right)^R-1=sum_R=1^Nr^R-1$$

You have
$$rS_N=rsum_R=1^Nr^R-1=sum_R=1^Nr^R$$
Then
$$S(r-1)=rS-S=sum_R=1^Nr^R-sum_R=1^Nr^R-1=cdots=r^N-r^0$$
So
$$S=dfrac1-r^N1-r=frac32left(1-frac13^Nright)$$

share|cite|improve this answer

answered Jul 18 at 6:17

Karn Watcharasupat

3,8192426

Let $r=frac13$, and
$$S_N=sum_R=1^Nleft(frac13right)^R-1=sum_R=1^Nr^R-1$$

You have
$$rS_N=rsum_R=1^Nr^R-1=sum_R=1^Nr^R$$
Then
$$S(r-1)=rS-S=sum_R=1^Nr^R-sum_R=1^Nr^R-1=cdots=r^N-r^0$$
So
$$S=dfrac1-r^N1-r=frac32left(1-frac13^Nright)$$

share|cite|improve this answer

answered Jul 18 at 6:17

Karn Watcharasupat

3,8192426

share|cite|improve this answer

share|cite|improve this answer

answered Jul 18 at 6:17

Karn Watcharasupat

3,8192426

answered Jul 18 at 6:17

Karn Watcharasupat

3,8192426

answered Jul 18 at 6:17

Karn Watcharasupat

3,8192426

3,8192426

add a comment | 

add a comment |