Determine the convergence of the series from n=4 to ∞ of [1+(1/n)]^-n^2

Question

We need to use the root test to answer this question.

Answer 1

I don't think so! Try this:

e = lim [1 + (1/n)]ⁿ as n goes to infinity.

lim {[1 + (1/n)]ⁿ}^-n is simply lim e^-n as n -> infinity = 0