calculate the sum of (-1)^n (n/8^n)

i know fourier coefficients and bessels inequality how to evaluate this

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- Nov 23rd 2012, 10:55 PMprasumalternating series sum
calculate the sum of (-1)^n (n/8^n)

i know fourier coefficients and bessels inequality how to evaluate this - Nov 24th 2012, 03:38 AMsbhatnagarRe: alternating series sum
The sum, , can be evaluated by using only elementary techniques.

Let ...(1)

...(2)

Adding (1) and (2) gives the incredible result

so - Nov 24th 2012, 04:02 AMprasumRe: alternating series sum
i did not understand the step which produces the incredible result can yu please explain

- Nov 24th 2012, 04:45 AMsbhatnagarRe: alternating series sum
- Nov 24th 2012, 04:49 AMPlatoRe: alternating series sum