Question

is this series convergent

the series from n=0 to infinity of
(n^2+1)/(n^3+1)

i said it converged at n=1

Answer 1

I don't know what you mean by "converging at n=1". That is only one term of the series.

The terms approach 1/n for large n, and the series sum diverges, having the behavior of log n for large n. (Think of the integral of 1/x fom 1 to infinity)