# The value of the sum ∑ i = 3 6 i ( i + 2 ) . ### 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 22E
To determine

## To find: The value of the sum ∑i=36i(i+2).

Expert Solution

The value of the sum i=36i(i+2) is 122.

### 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 i=36i(i+2) expressed as follows.

i=36i(i+2)=[3(3+2)]+[4(4+2)]+[5(5+2)]+[6(6+2)]=[3(5)]+[4(6)]+[5(7)]+[6(8)]=15+24+35+48=122

Thus value of the sum i=36i(i+2) is 122.

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