Determine this ∑(n=0 to +∞) (1/n^2 +1)

Question

Please help determine the ∑_{(n=0 to ∞)} (1/(n² + 1)

Answer 1

try adding up a few partial sums. they seem to converge to 1

1/(1^2+ 1) + 1/(2^2 + 1) + 1/(3^2 + 1) + 1/(4^2 + 1) + ...

= 1/2 + 1/5 + 1/10 + 1/17 + ...

it gets closer and closer to .999...