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Geometric Series

  • Thread starter mattmannmf
  • Start date
  • #1
172
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{sigma} 2*(-1/4)^(n-1)

Could i treat this as a geometric series? i know geometric is in the form of ar^n but the n is (n-1)

my A=2
my r= -1/4
 

Answers and Replies

  • #2
33,484
5,174
Your series appears to be
[tex]\sum_{n = 1}^{\infty} 2 (-1/4)^{n - 1}[/tex]

Write a few terms of this series and see if you can adjust the starting index.
 
  • #3
172
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i have no idea what you mean by that
 
  • #4
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
14,916
19
{sigma} 2*(-1/4)^(n-1)

Could i treat this as a geometric series? i know geometric is in the form of ar^n but the n is (n-1)

my A=2
my r= -1/4
You have
2(-1/4)n-1
and you want
A rn-1
?

Why not set them equal and try solving for A and r?
 
  • #5
172
0
no... im trying to solve whether or not the series converges or diverges and then i have to determine the sum of the series... meaning where the series sums up to..
 
  • #6
Hurkyl
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Science Advisor
Gold Member
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Oh, my mistake. I thought the method you had wanted to use was to rewrite the summand in a standard form, and were stuck on how to do that rewrite.
 
  • #7
Char. Limit
Gold Member
1,204
14
Well, just change n-1 into n using exponent rules.
 
  • #8
33,484
5,174
Write a few terms of the series and you should quickly see that it is a geometric series. A geometric series is one for which each term is a constant multiple of the previous term.
 

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