# The sum 1 + 3 + 5 + 7 + ⋯ + ( 2 n − 1 ) in sigma notation. ### 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 16E
To determine

## To write: The sum 1+3+5+7+⋯+(2n−1) in sigma notation.

Expert Solution

The sum 1+3+5+7++(2n1) expressed in sigma notation as i=1n(2i1).

### 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:

Here, the sum 1+3+5+7++(2n1) is the sum of n numbers and number is of the form 2i1, where i varies from 1 to n.

Thus, by the above definition the sum 1+3+5+7++(2n1) expressed as follows.

1+3+5+7++(2n1)=i=1n(2i1)

Thus, the sum 1+3+5+7++(2n1) expressed in sigma notation as i=1n(2i1).

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