Sequences & Series · Recursive sequence and series sum

Let

a_1 = 1

and for

n \ge 1

a_{n+1} = \dfrac12 a_n + \dfrac{n^2 - 2n - 1}{n^2(n+1)^2}

. Then

\left\lvert\displaystyle\sum_{n=1}^{\infty}\left(a_n - \frac{2}{n^2}\right)\right\rvert

is equal to .

Video solution coming soon

We're animating every PYQ step by step. Subscribe to get them first.