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sum[k=1,inf] 2/(k^2-1)

I applied the limit comparison test with 1/k^2

2* lim k->inf [ 1/(k^2-1) ] /(1/k^2) = 2*lim k->inf k^2/(k^2-1) =H 2

then because

sum[k=1,inf] 1/k^2 is a convergent p-series then sum[k=1,inf] 2/(k^2-1) must also converge by the limit comparison test.

I plugged this into wolfram alpha and it said that the sum does not converge. Am I doing something wrong? Thanks for any help.

This is what I put into wolfram alpha

sum[n=1,inf] of 2/(k^2-1)