calc..estimate the sum?

Question

determine whether the series is convergent or divergent using either the integral test or the comparison test:

1) summation notation symbol (with n=1 on bottom and infinity on top) of (ne)^-n

2) summation notation symbol (with n=1 on bottom and infinity on top) of ((cos^2)n)/(n^2 + 1)

3) summation notation symbol (with n=1 on bottom and infinity on top) of 1/ sqrt of (n^2 + 1)

show work/explanation so i know how u got the answer..thanks

Answer 1

1) (ne)^-n =1/n^n*e^n <1/e^n geometric series r =1/e Convergent
2) in abs val < 1/(n^2+1) of the same class as 1/n^2 Absolutely convergent
3) of the same class as 1/n as lim 1/n/1/sqrt(n^2+1)=1 Divergent