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April 29th, 2009, 02:13 PM   #1
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I'm confused with how to solve the limit of this series

the series is the summation from n=1 to infinite of 12/(-2)^n

I know the series converges but I can't figure out the sum. I originally thought it was a p-series, but it's not and I am just stumped right now.
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April 29th, 2009, 03:55 PM   #2
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Re: I'm confused with how to solve the limit of this series

Quote:
Originally Posted by Crystal-Field
the series is the summation from n=1 to infinite of 12/(-2)^n

I know the series converges but I can't figure out the sum. I originally thought it was a p-series, but it's not and I am just stumped right now.
It is a power series:
12( -1/2 +1/4 - 1/8 + ...) = 12([-1/2]/[1+1/2]) = -4
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April 29th, 2009, 04:59 PM   #3
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Re: I'm confused with how to solve the limit of this series

so then would it be

12(-1/2)^n

or would it be...

12(-1/2)^(-n)

and with that as a power series I could figure out the summation?
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April 29th, 2009, 06:12 PM   #4
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Re: I'm confused with how to solve the limit of this series

Quote:
Originally Posted by Crystal-Field
or would it be...

12(-1/2)^(-n)
No. That would then be 12(-2)^n. Study exponents. Either way, we call it here a Geometric Series.
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