# The value of the sum ∑ n = 1 20 ( − 1 ) n .

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter F, Problem 25E
To determine

## To find: The value of the sum ∑n=120(−1)n.

Expert Solution

The value of the sum n=120(1)n is 0.

### Explanation of Solution

Definition used:

If am,am+1,...,an are real numbers and m and n are integers such that mn, then i=mnai=am+am+1+am+2++an1+an.

Calculation:

By the above definition, the sum n=120(1)n expressed as follows.

n=120(1)n={(1)1+(1)2+(1)3+(1)4+(1)5+(1)6+(1)7+(1)8+(1)9+(1)10++(1)11+(1)12+(1)13+(1)14+(1)15+(1)16+(1)17+(1)18+(1)19+(1)20}=1+11+11+11+11+11+11+11+11+11+1=0

Thus value of the sum n=120(1)n is 0.

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