Does the series sum[k=1,inf] 2/(k^2-1) converge or diverge?

[GreenPrint]

Determine weather or not the following series converges or diverges.

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)

 

[Dick]

Determine weather or not the following series converges or diverges.

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)

Oh, I see what you are doing. Do you really mean [n=1,inf]?? n?? And the k=1 term of your series is undefined. Skip it.

 

[GreenPrint]

so I changed it to
sum[k=1,inf] of 2/(k^2-1)
and it says the sum does not converge

 

[Dick]

so I changed it to
sum[k=1,inf] of 2/(k^2-1)
and it says the sum does not converge

I told you. The k=1 term is undefined. That's probably WA's problem with that one.

 

[GreenPrint]

I told you. The k=1 term is undefined. That's probably WA's problem with that one.

Oh. Thanks.

 

[Mark44]

I told you. The k=1 term is undefined. That's probably WA's problem with that one.

Might be a case of GIGO, or "garbage in, garbage out."