energy of a sequence - absolutely summable sequence or square summable sequence

caramello

Hi,

I was doing some practise on the inverse DTFT and already derive the sequence. But then the question asks about the energy of the sequence. Let's say the sequence that I got is x(n) = [sin (pi/4 n)] / [(pi) (n)]. To find the energy, I already found something like 2 * sum from n=1 to infinity of [sin²(pi/4 n)] / [pi² n²] but then after that I was stuck, and I don't know how to solve the summation. Can someone help me with this?

Also, how do we know if a sequence is absolutely summable or if it is square-summable from the energy?

Thank you so much!