The sum x + x 2 + x 3 + ⋯ + x n 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 19E
To determine

To write: The sum x+x2+x3+⋯+xn in sigma notation.

Expert Solution

The sum x+x2+x3++xn expressed in sigma notation as i=1nxi.

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 x+x2+x3++xn is the sum of n  numbers and number is of the form xi, where i varies from 0 to n.

Thus, by the above definition the sum x+x2+x3++xn expressed as follows.

x+x2+x3++xn=i=1nxi

Thus, the sum x+x2+x3++xn expressed in sigma notation as i=1nxi.

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