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mathmathmad

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## Homework Statement

evaluate ∑ n^2.x^n where 0<x<1

## Homework Equations

## The Attempt at a Solution

let a_n = n^2 and c=0

then radius of convergence, R=1

hence the series convergences when |x|<1

let f(x) = ∑ n^2.x^n

then f'(x) = ∑ n^3.x^n-1 for n=0 to infinity

then f'(x) = ∑ (n+1)^3.x^n for n=1 to infinity

from here, how to I derive a function

**∑ (n+1)^3.x^n**so as to integrate it to get the sum?