[Calculus] Find The Sum of the Series ∞∑n = 0 (-1)^n (1/16)^n-1 / 2n+1

Question

Find the sum of the series: ∑^∞_n=0 (-1)ⁿ (1/16)^n-1 / 2n+1

Answer 1

The solution is 64tan^-1(1/4). You can get there by a little manipulation if arc tan is one of your "stock" Taylor series. If you divide by 64 you'll see the series in terms of powers of 1/4.