why does this converge to 0.

Hello,

problem is: An = ( cos(n*pi) )/n

I thought this problem would converge to -1 since cos(pi) equals -1

the answer is that it converges to 0.

Is this because of the Monotonic Rule, which states that it will converge to an unknown limit that can be its lower bound or less.

in other words, it was possible that this could have converged to -1, but instead it converged to 0?

I solved this problem by dividing by the greatest n in the denominator.

any help, please.

thanks.