does this series converge or diverge?

n = 2 E infinity

2/(n^2 -1)

..i've attempted to solve this, and i know the answer is 3/2

just not sure why i could not divide the numerator and denominator by the largest exponent in the denominator (n^2). is that because its not in the form of infininty/infinity?

also, tried using summation notation, it did not work out.

i know it can't be the harmonic series because that would diverge.

need some help please.