BuyFindarrow_forward

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Solutions

Chapter
Section
BuyFindarrow_forward

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

Evaluating a Sum In Exercises 25-28, use the summation formulas to rewrite the expression without the summation notation. Use the result to find the sums for n = 10 , 100 , 1000 , and 10,000.

i = 1 n 2 i + 1 n 2

To determine

To calculate: Sum of the expression i=1n2i+1n2 usingsummation formulas.

Explanation

Given: i=1n2i+1n2

Formula used: Formula for the sum of n natural number:

i=1ni=n(n+1)2

n times sum of constant is given as:

i=1nc=nc

Calculation: Consider the provided expression.

i=1n2i+1n2

To apply summation formula, split the expression in two parts:

i=1n2i+1n2=i=1n2in2+i=1n1n2

Factor out 2n2 from first summation and 1n2 from second summation:

i=1n2in2+i=1n1n2=2n2i=1ni+1n2i=1n1

Apply the formulas for summation:

i=1ni=n(n+1)2 and i=1nc=nc

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
Sect-4.1 P-11ESect-4.1 P-12ESect-4.1 P-13ESect-4.1 P-14ESect-4.1 P-15ESect-4.1 P-17ESect-4.1 P-16ESect-4.1 P-19ESect-4.1 P-20ESect-4.1 P-18ESect-4.1 P-27ESect-4.1 P-28ESect-4.1 P-23ESect-4.1 P-24ESect-4.1 P-25ESect-4.1 P-26ESect-4.1 P-29ESect-4.1 P-30ESect-4.1 P-21ESect-4.1 P-22ESect-4.1 P-33ESect-4.1 P-34ESect-4.1 P-35ESect-4.1 P-36ESect-4.1 P-31ESect-4.1 P-32ESect-4.1 P-37ESect-4.1 P-38ESect-4.1 P-39ESect-4.1 P-40ESect-4.1 P-41ESect-4.1 P-42ESect-4.1 P-43ESect-4.1 P-44ESect-4.1 P-45ESect-4.1 P-46ESect-4.1 P-47ESect-4.1 P-48ESect-4.1 P-49ESect-4.1 P-50ESect-4.1 P-51ESect-4.1 P-52ESect-4.1 P-53ESect-4.1 P-54ESect-4.1 P-55ESect-4.1 P-56ESect-4.1 P-57ESect-4.1 P-58ESect-4.1 P-59ESect-4.1 P-60ESect-4.1 P-61ESect-4.1 P-62ESect-4.1 P-63ESect-4.1 P-64ESect-4.1 P-65ESect-4.1 P-66ESect-4.1 P-67ESect-4.1 P-68ESect-4.1 P-69ESect-4.1 P-70ESect-4.1 P-71ESect-4.1 P-72ESect-4.1 P-73ESect-4.1 P-74ESect-4.1 P-79ESect-4.1 P-80ESect-4.1 P-75ESect-4.1 P-76ESect-4.1 P-77ESect-4.1 P-81ESect-4.1 P-78ESect-4.2 P-1ESect-4.2 P-2ESect-4.2 P-3ESect-4.2 P-4ESect-4.2 P-5ESect-4.2 P-6ESect-4.2 P-7ESect-4.2 P-8ESect-4.2 P-9ESect-4.2 P-10ESect-4.2 P-11ESect-4.2 P-12ESect-4.2 P-13ESect-4.2 P-14ESect-4.2 P-15ESect-4.2 P-16ESect-4.2 P-17ESect-4.2 P-18ESect-4.2 P-19ESect-4.2 P-20ESect-4.2 P-21ESect-4.2 P-22ESect-4.2 P-23ESect-4.2 P-24ESect-4.2 P-25ESect-4.2 P-26ESect-4.2 P-27ESect-4.2 P-28ESect-4.2 P-29ESect-4.2 P-30ESect-4.2 P-31ESect-4.2 P-32ESect-4.2 P-33ESect-4.2 P-34ESect-4.2 P-35ESect-4.2 P-36ESect-4.2 P-37ESect-4.2 P-38ESect-4.2 P-39ESect-4.2 P-40ESect-4.2 P-41ESect-4.2 P-42ESect-4.2 P-43ESect-4.2 P-44ESect-4.2 P-45ESect-4.2 P-46ESect-4.2 P-47ESect-4.2 P-48ESect-4.2 P-49ESect-4.2 P-50ESect-4.2 P-51ESect-4.2 P-52ESect-4.2 P-53ESect-4.2 P-54ESect-4.2 P-55ESect-4.2 P-56ESect-4.2 P-57ESect-4.2 P-58ESect-4.2 P-59ESect-4.2 P-60ESect-4.2 P-61ESect-4.2 P-62ESect-4.2 P-63ESect-4.2 P-64ESect-4.2 P-65ESect-4.2 P-66ESect-4.2 P-67ESect-4.2 P-68ESect-4.2 P-69ESect-4.2 P-70ESect-4.2 P-71ESect-4.2 P-72ESect-4.2 P-73ESect-4.2 P-74ESect-4.2 P-75ESect-4.2 P-76ESect-4.2 P-77ESect-4.2 P-78ESect-4.2 P-79ESect-4.3 P-1ESect-4.3 P-2ESect-4.3 P-3ESect-4.3 P-4ESect-4.3 P-5ESect-4.3 P-6ESect-4.3 P-7ESect-4.3 P-8ESect-4.3 P-9ESect-4.3 P-10ESect-4.3 P-11ESect-4.3 P-12ESect-4.3 P-13ESect-4.3 P-14ESect-4.3 P-15ESect-4.3 P-16ESect-4.3 P-17ESect-4.3 P-18ESect-4.3 P-19ESect-4.3 P-20ESect-4.3 P-21ESect-4.3 P-22ESect-4.3 P-23ESect-4.3 P-24ESect-4.3 P-25ESect-4.3 P-26ESect-4.3 P-27ESect-4.3 P-28ESect-4.3 P-29ESect-4.3 P-30ESect-4.3 P-31ESect-4.3 P-32ESect-4.3 P-33ESect-4.3 P-34ESect-4.3 P-35ESect-4.3 P-36ESect-4.3 P-37ESect-4.3 P-38ESect-4.3 P-39ESect-4.3 P-40ESect-4.3 P-41ESect-4.3 P-42ESect-4.3 P-43ESect-4.3 P-44ESect-4.3 P-45ESect-4.3 P-46ESect-4.3 P-47ESect-4.3 P-48ESect-4.3 P-49ESect-4.3 P-50ESect-4.3 P-51ESect-4.3 P-52ESect-4.3 P-53ESect-4.3 P-54ESect-4.3 P-55ESect-4.3 P-56ESect-4.3 P-57ESect-4.3 P-58ESect-4.3 P-59ESect-4.3 P-60ESect-4.3 P-61ESect-4.3 P-62ESect-4.3 P-63ESect-4.3 P-64ESect-4.3 P-65ESect-4.3 P-66ESect-4.3 P-67ESect-4.3 P-68ESect-4.3 P-69ESect-4.3 P-70ESect-4.3 P-71ESect-4.3 P-72ESect-4.3 P-73ESect-4.3 P-74ESect-4.3 P-75ESect-4.3 P-76ESect-4.3 P-77ESect-4.3 P-78ESect-4.3 P-79ESect-4.4 P-1ESect-4.4 P-2ESect-4.4 P-3ESect-4.4 P-4ESect-4.4 P-5ESect-4.4 P-6ESect-4.4 P-7ESect-4.4 P-8ESect-4.4 P-9ESect-4.4 P-12ESect-4.4 P-10ESect-4.4 P-11ESect-4.4 P-13ESect-4.4 P-14ESect-4.4 P-15ESect-4.4 P-16ESect-4.4 P-17ESect-4.4 P-18ESect-4.4 P-19ESect-4.4 P-20ESect-4.4 P-21ESect-4.4 P-22ESect-4.4 P-23ESect-4.4 P-24ESect-4.4 P-25ESect-4.4 P-26ESect-4.4 P-27ESect-4.4 P-28ESect-4.4 P-29ESect-4.4 P-30ESect-4.4 P-31ESect-4.4 P-32ESect-4.4 P-33ESect-4.4 P-34ESect-4.4 P-35ESect-4.4 P-36ESect-4.4 P-37ESect-4.4 P-38ESect-4.4 P-39ESect-4.4 P-40ESect-4.4 P-41ESect-4.4 P-42ESect-4.4 P-43ESect-4.4 P-45ESect-4.4 P-44ESect-4.4 P-46ESect-4.4 P-47ESect-4.4 P-48ESect-4.4 P-49ESect-4.4 P-50ESect-4.4 P-51ESect-4.4 P-52ESect-4.4 P-53ESect-4.4 P-54ESect-4.4 P-55ESect-4.4 P-56ESect-4.4 P-57ESect-4.4 P-58ESect-4.4 P-59ESect-4.4 P-60ESect-4.4 P-61ESect-4.4 P-62ESect-4.4 P-63ESect-4.4 P-64ESect-4.4 P-65ESect-4.4 P-66ESect-4.4 P-67ESect-4.4 P-68ESect-4.4 P-69ESect-4.4 P-70ESect-4.4 P-71ESect-4.4 P-72ESect-4.4 P-73ESect-4.4 P-74ESect-4.4 P-75ESect-4.4 P-76ESect-4.4 P-77ESect-4.4 P-78ESect-4.4 P-79ESect-4.4 P-80ESect-4.4 P-81ESect-4.4 P-82ESect-4.4 P-83ESect-4.4 P-84ESect-4.4 P-85ESect-4.4 P-86ESect-4.4 P-87ESect-4.4 P-88ESect-4.4 P-89ESect-4.4 P-90ESect-4.4 P-91ESect-4.4 P-92ESect-4.4 P-93ESect-4.4 P-94ESect-4.4 P-95ESect-4.4 P-96ESect-4.4 P-97ESect-4.4 P-98ESect-4.4 P-99ESect-4.4 P-100ESect-4.4 P-101ESect-4.4 P-102ESect-4.4 P-103ESect-4.4 P-104ESect-4.4 P-105ESect-4.4 P-106ESect-4.4 P-107ESect-4.4 P-108ESect-4.4 P-109ESect-4.4 P-110ESect-4.4 P-111ESect-4.4 P-112ESect-4.4 P-113ESect-4.4 P-114ESect-4.4 P-115ESect-4.5 P-1ESect-4.5 P-2ESect-4.5 P-3ESect-4.5 P-4ESect-4.5 P-5ESect-4.5 P-6ESect-4.5 P-7ESect-4.5 P-8ESect-4.5 P-9ESect-4.5 P-10ESect-4.5 P-11ESect-4.5 P-12ESect-4.5 P-13ESect-4.5 P-14ESect-4.5 P-15ESect-4.5 P-16ESect-4.5 P-17ESect-4.5 P-19ESect-4.5 P-18ESect-4.5 P-20ESect-4.5 P-21ESect-4.5 P-22ESect-4.5 P-23ESect-4.5 P-24ESect-4.5 P-25ESect-4.5 P-26ESect-4.5 P-27ESect-4.5 P-28ESect-4.5 P-29ESect-4.5 P-30ESect-4.5 P-31ESect-4.5 P-32ESect-4.5 P-33ESect-4.5 P-34ESect-4.5 P-35ESect-4.5 P-36ESect-4.5 P-37ESect-4.5 P-38ESect-4.5 P-39ESect-4.5 P-40ESect-4.5 P-41ESect-4.5 P-42ESect-4.5 P-43ESect-4.5 P-44ESect-4.5 P-45ESect-4.5 P-46ESect-4.5 P-47ESect-4.5 P-48ESect-4.5 P-51ESect-4.5 P-52ESect-4.5 P-49ESect-4.5 P-50ESect-4.5 P-53ESect-4.5 P-54ESect-4.5 P-55ESect-4.5 P-56ESect-4.5 P-57ESect-4.5 P-58ESect-4.5 P-59ESect-4.5 P-60ESect-4.5 P-71ESect-4.5 P-72ESect-4.5 P-61ESect-4.5 P-62ESect-4.5 P-63ESect-4.5 P-64ESect-4.5 P-65ESect-4.5 P-66ESect-4.5 P-67ESect-4.5 P-68ESect-4.5 P-69ESect-4.5 P-70ESect-4.5 P-73ESect-4.5 P-74ESect-4.5 P-75ESect-4.5 P-76ESect-4.5 P-77ESect-4.5 P-78ESect-4.5 P-79ESect-4.5 P-80ESect-4.5 P-81ESect-4.5 P-82ESect-4.5 P-83ESect-4.5 P-84ESect-4.5 P-85ESect-4.5 P-86ESect-4.5 P-87ESect-4.5 P-88ESect-4.5 P-89ESect-4.5 P-90ESect-4.5 P-91ESect-4.5 P-92ESect-4.5 P-93ESect-4.5 P-94ESect-4.5 P-95ESect-4.5 P-96ESect-4.5 P-97ESect-4.5 P-98ESect-4.5 P-99ESect-4.5 P-100ESect-4.5 P-101ESect-4.5 P-102ESect-4.5 P-103ESect-4.5 P-104ECh-4 P-1RECh-4 P-2RECh-4 P-3RECh-4 P-4RECh-4 P-5RECh-4 P-8RECh-4 P-6RECh-4 P-7RECh-4 P-9RECh-4 P-10RECh-4 P-11RECh-4 P-12RECh-4 P-13RECh-4 P-14RECh-4 P-15RECh-4 P-16RECh-4 P-17RECh-4 P-18RECh-4 P-21RECh-4 P-22RECh-4 P-23RECh-4 P-24RECh-4 P-19RECh-4 P-20RECh-4 P-27RECh-4 P-28RECh-4 P-29RECh-4 P-30RECh-4 P-31RECh-4 P-32RECh-4 P-25RECh-4 P-26RECh-4 P-33RECh-4 P-34RECh-4 P-35RECh-4 P-36RECh-4 P-37RECh-4 P-38RECh-4 P-39RECh-4 P-40RECh-4 P-43RECh-4 P-46RECh-4 P-41RECh-4 P-42RECh-4 P-49RECh-4 P-52RECh-4 P-44RECh-4 P-45RECh-4 P-53RECh-4 P-54RECh-4 P-55RECh-4 P-56RECh-4 P-47RECh-4 P-48RECh-4 P-57RECh-4 P-58RECh-4 P-50RECh-4 P-51RECh-4 P-60RECh-4 P-59RECh-4 P-63RECh-4 P-61RECh-4 P-62RECh-4 P-64RECh-4 P-65RECh-4 P-66RECh-4 P-67RECh-4 P-68RECh-4 P-69RECh-4 P-70RECh-4 P-71RECh-4 P-72RECh-4 P-73RECh-4 P-74RECh-4 P-75RECh-4 P-76RECh-4 P-1PSCh-4 P-2PSCh-4 P-14PSCh-4 P-5PSCh-4 P-6PSCh-4 P-7PSCh-4 P-8PSCh-4 P-9PSCh-4 P-10PSCh-4 P-11PSCh-4 P-12PSCh-4 P-13PSCh-4 P-15PSCh-4 P-16PSCh-4 P-17PSCh-4 P-3PSCh-4 P-4PSCh-4 P-18PSCh-4 P-19PSCh-4 P-20PSCh-4 P-21PS

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

Expand each expression in Exercises 122. (3x+1)(2x2x+1)

Finite Mathematics and Applied Calculus (MindTap Course List)

Calculate y'. 47. y = cosh1(sinh x)

Calculus: Early Transcendentals

In Exercises 4954, find an equation of the line that satisfies the given condition. 49. The line parallel to th...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Solve each equation: n26n60=0

Elementary Technical Mathematics

In Exercises 14, find the distance between the two points. (2,1) and (6,4)

Finite Mathematics for the Managerial, Life, and Social Sciences

0 1 does not exist

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

For , f′(x) =

Study Guide for Stewart's Multivariable Calculus, 8th

Simplify each expression. lne4

College Algebra (MindTap Course List)