# The value of the sum ∑ i = 1 n ( 2 − 5 i ) . ### 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 30E
To determine

## To find: The value of the sum ∑i=1n(2−5i).

Expert Solution

The value of the sum i=1n(25i) is n(5n+1)2.

### 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.

Theorem used:

Let c be a constant and n be a positive integer. Then,

i=1nc=nc, i=1ni=n(n+1)2 and i=1ni2=n(n+1)(2n+1)6.

Calculation:

By the above definition, the sum i=1n(25i) expressed as follows.

i=1n(25i)=i=1n25i=1ni=2n5(n(n+1)2)=4n5n25n2=n(5n+1)2

Thus value of the sum i=1n(25i) is n(5n+1)2.

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