The original series (-1 is raised to the n+3 power. Couldn't figure out how to raise more than just the bracket with LaTeX):
I took everything except the (-1)^n+3 part, and called it bn. In order for the series to be convergent, bn must:
1. be decreasing
2. have a limit of 0 when n->inf
bn+1 is less than bn, so it is obviously decreasing.
And the limit is obviously 0, because the denominator will grow while the numerator stays 1.
Am I correct? Also, what does it mean to be "absolute" and "conditionally" convergent? Which one is this?