# The sum ∑ i = 1 n 3 2 i − 1 .

### 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 48E
To determine

## To evaluate: The sum ∑i=1n32i−1.

Expert Solution

The value of the sum i=1n32i1 is 6[1(12)n].

### Explanation of Solution

The formula for the sum of a finite geometric serious with first term a and common ratio r1, is i=1nari1=a+ar+ar2++arn1=a(rn1)r1.

Here, the sum i=1n32i1 is in the form i=1nari1 where, a=3andr=12.

By the above formula, the value of the sum is simplified as,

i=1n32i1=3[(12)n1](12)1=3[(12)n1](12)=6[1(12)n]

Thus, the value of the sum i=1n32i1 is 6[1(12)n].

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