Question

f(x) = summation from n = 1 to ∞ of (x^n)((n + 1) / 4^(n +1)) with an interval of convergence, –4 < x < 4.
Find exactly the value of the integral from 0 to 2 of f(x), dx. Your answer will be a positive integer.

ALSO: Can you please take me through every step until you reach the ANSWER because I'm having trouble understanding this?
Thank you!

Answer 1

This article should prove helpful in relating the sum to the integral.

https://www.emathhelp.net/calculators/calculus-2/series-calculator/?f=%28n%2B1%29%2F4%5E%28n%2B1%29+x%5En&var=n&a=1&b=inf