Convergence & Divergence

Which of the following series Diverge?
I.  $\sum_{n=1}^{\infty}\frac{1}{n^2}$      II.  $\sum_{n=1}^{\infty}\frac{1}{n}$      III.  $\sum_{n=1}^{\infty}\frac{1}{\sqrt{n}}$  

• I

• II

• II and III

• I and III

 $\sum_{n=1}^{\infty}\frac{1}{n^2}$  can be used to determine the convergence or divergence  with a limit comparison test for which series?

•  $\sum_{n=1}^{\infty}\frac{n}{n^3+n^2}$  

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

•  $\sum_{n=1}^{\infty}\frac{1}{\sqrt{n^4+2n}}$  

• all of the above

Which of the following series should you use the ratio test to determine convergence or divergence?

• $\sum_{n=1}^{\infty}\frac{n^2+n}{3n^2+5}$

• $\sum_{n=1}^{\infty}\frac{n^n}{n!}$

• $\sum_{n=1}^{\infty}\frac{\ln\ n}{n}$

• $\sum_{n=1}^{\infty}\frac{1}{2^n}$

Which series diverges by the nth term test?

• $\sum_{n=1}^{\infty}\frac{n}{n!}$

• $\sum_{n=1}^{\infty}\frac{3^n}{5^n}$

• $\sum_{n=1}^{\infty}\frac{5n^2}{3n^3+n^2}$

• $\sum_{n=1}^{\infty}\frac{1}{\tan^{-1}n}$

Which series can the integral test be used to determine convergence or divergence?

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

• $\sum_{n=1}^{\infty}\frac{\ln n}{n}$

• $\sum_{n=1}^{\infty}\frac{\sin^{-1}n}{\sqrt{1-n^2}}$

• all of the above