# Series problems -Comparison Tests

1. Mar 29, 2009

Series problems --Comparison Tests

1. The problem statement, all variables and given/known data

Are the following series convergent or divergent?

a. summation (n=1 to infinity) (n-1) / (n^2 * n^(1/2))

b. summation (n=1 to infinity) (n+4^n) / (n+6^n)

c. summation (n=1 to infinity) (n+5) / [(n^7 + n^2)^(1/3)]

2. Relevant equations

Exclusive use of comparison test and/or limit comparison test

3. The attempt at a solution

a. I assume convergence since 1/n term factored out. But, the problem I have here is that n-1 / (n^2 * n^1/2) is less than 1/n so how can n=1 (by the p-test) be convergent?