CPM Homework Help : CALC Problem 12-108

Consider the infinite series below. For each series, decide if it diverges, converges conditionally, or converges absolutely and justify your conclusion. State the test you used. Homework Help ✎

Step (a):

$=\sum_{n=1}^\infty \frac{1}{n^2+2}$

Step (b):

$=\sum_{n=1}^\infty \frac{1}{n^3+1}$

Step (c):

$= \ln(1)-\ln(2)+\ln(2)-\ln(3)+\ln(3)-\ln(4)+...$

Hint (d):

Think of this as two separate series:

$\frac{-2}{1}+\frac{-2}{3}+\frac{-2}{5}+...\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+...$