I'm just starting to study limits of sequences and have been asked to determine if the series;

Sum (n=1 --> n = inf) 1/((n^2)+1) converges or diverges,

Is it correct for me to do the following,

Series will converge if the sequence (1/((n^2)+1) converges, hence;

take lim (n-->inf) (1/((n^2)+1)

and the limit = 0 as 1/inf is 0 in the limit.

?? is this correct? and should i be able to calculate the actual limit.

Cheers.