Calculus II Integral test

Question

Use the integral test do determine if

infinity

Sigma 1/(n(lnn)^5/4)

n = 3

converges or diverges. Assume that the requirements for integral test are met.

Answer 1

If your denominator is n (ln n)^5/4, then you should make the substitution y = ln n

which converts the integral to y^-5/4 dy between ln 3 and ∞.

The integral then is y^-1/4/(-1/4) between ln 3 and ∞.

This evaluates to (ln 3)/4 which is close to 1/4.

Therefore the series converges.

If you denominator is not as described, all bets are off!