Question

Question #37d69

Answer 1

See below.

Explanation:

We have

`int_2^n lnx/x^2 dx = 1/2+ln2/2-1/n-ln n/n ge sum_(k=2)^n ln k/k^2`

but

`lim_(n->oo)1/2+ln2/2-1/n-ln/n = 1/2+ln2/2 ge sum_(k=2)^oo ln k/k^2`

so it converges.