Opener: Determine if the following series converges or diverges.
∞
n+n
∑ n3
n=1
2
Goal: to use the Integral Test to determine convergence or
divergence of an infinite series.
nth Term Test for Divergence
Geometric Series
Telescoping Series
Harmonic Series
______________________
1. Determine if the following series converges or diverges.
∞
n
∑ n2 + 1
n=1
2. Determine if the following series converges or diverges.
∞
n
∑ n +1
n=1
3. Determine if the following series converges or diverges.
∞
en
∑ 1+ e2n
n=1
4. Determine if the following series converges or diverges.
∞
2n
∑ 3n
n=1
5. Determine if the following series converges or diverges.
∞
2
∑ n +1
n=1
6. For what values of P does a P-Series converge? diverge?
∞
1
1 1
1
1
∑ n p = 1p + 2 p + 3p +!+ n p
n=1
∫
∞
1
dx
xp