# The sum ∑ j = 0 n − 1 ( − 1 ) j is in expanded form. ### 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 9E
To determine

## To write: The sum ∑j=0n−1(−1)j is in expanded form.

Expert Solution

The expanded form of the sum j=0n1(1)j is 11+11++(1)n1.

### 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 expression j=0n1(1)j simplified as follows.

j=0n1(1)j=(1)0+(1)1+(1)2+(1)3++(1)n1=11+11++(1)n1

Thus, the expanded form of the sum j=0n1(1)j is 11+11++(1)n1.

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