   Chapter 4, Problem 11PS

Chapter
Section
Textbook Problem

Riemann Sum Use an appropriate Riemann sum to evaluate the limit lim n → ∞ 1 + 2 + 3 + ⋯ + n n 3 / 2 .

To determine

To calculate: The sum of limn1+2+...+nn32 by usingsuitable Riemann sum.

Explanation

Given:

The expression is: limn1+2+...+nn32

Formula used:

Thefunction f(x)‘s Riemann sum on [ 0,1 ] is:

S(n)=i=1nf(ci)Δx=i=1nf(in)1n

Calculation:

Considering the sum:

limn1+2+...+nn32=limn[ i=1nin32 ]…… (1)

Consideringany integral function f(x) on [ 0,1 ] and separating the interval with n subintervals having width,

Δx=10n=1n

Considering the right end points of all intervals as,

ci=0+i(1n)

Hence, the function f(x)’s Riemann sum on [ 0,1 ] is:

S(n)=i=

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Solve the equations in Exercises 126. x69x4=0

Finite Mathematics and Applied Calculus (MindTap Course List)

Evaluate the integral. 7. 0/2cos2d

Calculus: Early Transcendentals

In Problems 45-51, solve each system of equations. 48.

Mathematical Applications for the Management, Life, and Social Sciences

Write each expression in terms of i. 18

Trigonometry (MindTap Course List)

Finding a Limit In Exercises 5166, find the limit. limx02xx2+4x

Calculus: Early Transcendental Functions (MindTap Course List) 