Limits of Sequences

Practice Questions

GRE Subject Test: Math › Limits of Sequences

Questions

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

Find the radius of convergence for the power series

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

Calculate the sum of the following infinite geometric series:

$\sum_{k=0}^{\infty}17\left(\frac{1}{6}\right)^k$

You have a divergent series $\sum_{n=1}^{\infty} a_{n}$ , and you multiply it by a constant 10. Is the new series $\sum_{n=1}^{\infty}10* a_{n}$ convergent or divergent?

Determine how many terms need to be added to approximate the following series within $\frac{1}{1000}$ :

$\sum_{n=1}^{\infty} (-1)^n\frac{4}{(n!)^2}$

Determine if the following series is divergent, convergent or neither.

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

There are 2 series $\sum_{n=1}^{\infty} \left(\frac{3}{7}\right)^n$ and $\sum_{n=1}^{\infty}\left(\frac{5}{11}\right)^n$ .

Is the sum of these 2 infinite series convergent, divergent, or inconclusive?

There are 2 series, $\sum_{n=1}^{\infty}a_{n}$ and $\sum_{n=1}^{\infty}b_{n}$ , and they are both convergent. Is $\sum_{n=1}^{\infty}a_{n} + \sum_{n=1}^{\infty}b_{n}$ convergent, divergent, or inconclusive?

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