# The value of the sum ∑ k = 0 8 cos k π .

### 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 24E
To determine

## To find: The value of the sum ∑k=08coskπ.

Expert Solution

The value of the sum k=08coskπ is 1.

### 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 k=08coskπ expressed as follows.

k=08coskπ={cos(0π)+cos(1π)+cos(2π)+cos(3π)+cos(4π)+cos(5π)+cos(6π+)+cos(7π)+cos(8π)}=11+11+11+11+1=1

Thus value of the sum k=08coskπ is 1.

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