Determine the convergence of the series ∑n=1∞(−1)nnp+(−1)n\sum_{n=1}^{\infty} \frac{(-1)^n}{n^p + (-1)^n}∑n=1∞np+(−1)n(−1)n for p>0p > 0p>0.
Converges for all p>0p > 0p>0
Converges only if p>1p > 1p>1
Diverges for all p>0p > 0p>0
Converges only if p>0.5p > 0.5p>0.5