# The sum ∑ i = 1 n f ( x i ) Δ x i is in expanded form. ### 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 10E
To determine

## To write: The sum ∑i=1nf(xi)Δxi is in expanded form.

Expert Solution

The expanded form of the sum i=1nf(xi)Δxi is f(x1)Δx1+f(x2)Δx2+f(x3)Δx3++f(xn)Δxn.

### 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 expression i=1nf(xi)Δxi simplified as follows.

i=1nf(xi)Δxi=f(x1)Δx1+f(x2)Δx2+f(x3)Δx3++f(xn)Δxn

Thus, the expanded form of the sum i=1nf(xi)Δxi is f(x1)Δx1+f(x2)Δx2+f(x3)Δx3++f(xn)Δxn.

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