Sequences & Series

Practice Questions

GRE Subject Test: Math › Sequences & Series

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1

Evaluate: $\large \large \sum_{x=1}^{10} \frac {1}{n}$ . (Round to 4 places)

2

Find the radius of convergence for the power series

$\small \sum_{n=0}^{\infty}\frac{(n!)^2x^n}{(2n)!}$

3

Evaluate: $\large \large \sum_{x=1}^{10} \frac {1}{n}$ . (Round to 4 places)

4

Assuming that $a_{n}=n^{\alpha}(n+1)$ , $\alpha \ge 2$ . Using the ratio test, what can we say about the series:

$\sum_{n=1}^{\infty} \frac{1}{a_{n}}$

5

Find the radius of convergence for the power series

$\small \sum_{n=0}^{\infty}\frac{(n!)^2x^n}{(2n)!}$

6

Evaluate: $\large \large \sum_{x=1}^{10} \frac {1}{n}$ . (Round to 4 places)

7

Assuming that $a_{n}=n^{\alpha}(n+1)$ , $\alpha \ge 2$ . Using the ratio test, what can we say about the series:

$\sum_{n=1}^{\infty} \frac{1}{a_{n}}$

8

Assuming that $a_{n}=n^{\alpha}(n+1)$ , $\alpha \ge 2$ . Using the ratio test, what can we say about the series:

$\sum_{n=1}^{\infty} \frac{1}{a_{n}}$

9

Find the radius of convergence for the power series

$\small \sum_{n=0}^{\infty}\frac{(n!)^2x^n}{(2n)!}$

10

If the first term of an arithmetic sequence is 2 and the third term is 8, find the $\large \large 16$ th term.

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