Question

I am trying to use the nth term test to determine if the series sum (n=1 to infinity ) of (n^2 +1)/n^2 converges or diverges, can someone help me out?

Answer 1

Have you considered that \(\dfrac{n^{2} + 1}{n^{2}} = 1 + \dfrac{1}{n^{2}}\)

Answer 2

Dear MR: I don't quite recognize your term, "nth term test." Mind explaining it?
However: tkhunny has a great suggestion above. Note that if n goes to infinity, a sub n goes to 1. Imagine yourself summing up hundred and thousands of 1's. Convergent? Divergent?

Answer 3

I didn't look at it that way, but that doss help immensely. Thanks!

Answer 4

It is a fundamental premise of convergence. If the individual terms do not approach ZERO, you're done. Divergence. If the individual terms DO approach zero, THEN there is something to talk about. ALWAYS check that first.

Answer 5

Upon further thought: perhaps you're talking about the "test for divergence" (not test for convergence). There is such a test. If the nth term of the series does not go to 0 as n approaches inf., the series diverges, which fits our initial conclusion.

Answer 6

tkhunny, my soul bro!!