I am having difficulty with calculating this sum.
By the Ratio Test, the series converges and on the solution key of the last year's exam it written that the sum = $\ln 3$.
I tried known Maclaurin Series but there is a problem every time. For example, when I try the expansion of $\arctan x$ I can't get rid of $(-1)^n.$
Could you help out, or give a hint?