Evaluate ∑n=1∞(n2+k−n)\sum_{n=1}^{\infty} \left( \sqrt{n^2+k} - n \right)∑n=1∞(n2+k−n) for k>0k > 0k>0.
Converges for all kkk
Diverges for all k>0k > 0k>0
Converges if k=1k=1k=1
Diverges for k=1k=1k=1