BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter F, Problem 29E
To determine

To find: The value of the sum i=1n2i.

Expert Solution

Answer to Problem 29E

The value of the sum i=1n2i is n(n+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 i=1n2i expressed as follows.

i=1n2i=2i=1ni=2(n(n+1)2)[i=1ni=n(n+1)2]=n(n+1)

Thus value of the sum i=1n2i is n(n+1).

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