I've been given the function $$f(x)=\sum_{n=0}^{\infty}(2n+1)(2x)^{2n}$$ And I have to evaluate $f(1/4)$ so find the value of $$f(1/4)=\sum_{n=0}^{\infty}\frac{2n+1}{2^{2n}}$$ I would appreciate any help with this as I am pretty lost.
Evaluating an infinite series
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calculus
sequences-and-series
power-series
taylor-expansion