Sequences and Series

Practice Questions

Pre-Calculus › Sequences and Series

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1

What is the sum of the alternating series below?

$10 - 5 + \frac{5}{2} - \frac{5}{4}+\frac{5}{8}-\frac{5}{16}+\cdots$

2

What is the sum of the following infinite series?

$S=2-\frac{1}{3}+1-\frac{1}{9} +\frac{1}{2}-\frac{1}{27}+\frac{1}{4}-\frac{1}{81}+\cdots$

3

Find the sum of the following infinite series:

$9 + 3 + 1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \frac{1}{81} + \frac{1}{243} + .....$

4

What is the sum of the alternating series below?

$10 - 5 + \frac{5}{2} - \frac{5}{4}+\frac{5}{8}-\frac{5}{16}+\cdots$

5

What is the sum of the following infinite series?

$S=2-\frac{1}{3}+1-\frac{1}{9} +\frac{1}{2}-\frac{1}{27}+\frac{1}{4}-\frac{1}{81}+\cdots$

6

Find the sum of the following infinite series:

$9 + 3 + 1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \frac{1}{81} + \frac{1}{243} + .....$

7

In the infinite series $a_{1}, a_{2}...a_{n},$ each term $a_{n}=(-2)^{n}$ such that the first two terms are and . What is the sum of the first eight terms in the series?

8

Rewrite this sum using summation notation:

9

In the infinite series $a_{1}, a_{2}...a_{n},$ each term $a_{n}=(-2)^{n}$ such that the first two terms are and . What is the sum of the first eight terms in the series?

10

Rewrite this sum using summation notation:

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