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f(x)=sum from n=0 to inf. of ((-1)^n) * (n+1)/(5n) * (x^n).

Find the integral from 0 to 1 of f(x) dx

I tried and got as far as the sum from 0 to inf of ((-1)^(n)) / (5n). the n=0 seems to be a problem as the first term is 1/0. Also, cant find the common ratio to use the formula to find the sum.

Please help me figure out the problem, will be greatly appreciated.

the sum from 1 to infinity of ((-1)^(n+1)) / (n^3)

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