Determine whether each of these series converge absolutely,
converge conditionally, or diverge.
n=1∑∞(−1)n+1n4+3n2n=1∑∞(−1)n−14n−13nn=1∑∞n4sin(n)n=42∑∞n7(−1)nn=1∑∞7n(−1)nn=1∑∞(−1)n3n+75nn=1∑∞ln(n2)(−1)n+4n=7∑∞(−1)n(n+7−n)
For what values of p is this series convergent?
n=2∑∞(−1)n−1n(ln(n))p