integration help?

Question

sum from 2 to inf of 1/(n*(ln n)^2)

I know use Integration but I get u=ln n and go till the end and I get
0+(1/ln2)
which converges or diverges or did I get that right?

Answer 1

are you asking if the series converges?
Using integral test,
you get -1/ln n and substituting the limits, you get 1/ln 2
since the integral converges, the series converges.

Answer 2

Let u = ln(n), du = dn/n
∫du/u^2) = - 1/u = -1/ln(n)
applying limits,
y = 0 + 1/ln(2) = 1.442695

Answer 3

so is this the sigma notation with upper limit inf and lower limit n = 2? i would suggest you could try partial fractions first then method of difference.