# The sum 1 − x + x 2 − x 3 + ⋯ + ( − 1 ) n x n in sigma notation.

### 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 20E
To determine

## To write: The sum 1−x+x2−x3+⋯+(−1)nxn in sigma notation.

Expert Solution

The sum 1x+x2x3++(1)nxn expressed in sigma notation as i=1n(1)nxi.

### 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:

Here, the sum 1x+x2x3++(1)nxn is the sum of n numbers and number is of the form (1)nxi, where i varies from 0 to n.

Thus, by the above definition the sum 1x+x2x3++(1)nxn expressed as follows.

1x+x2x3++(1)nxn=i=1n(1)nxi

Thus, the sum 1x+x2x3++(1)nxn expressed in sigma notation as i=1n(1)nxi.

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