Calculus 11th Edition - Ron LarsonChapter 4.2 - Area"Evaluating a Sum". Use the properties of summation and Theorem 4.2 to evaluate the sum. Use the summation capabilities of a graphing utility to verify your result. Please show work and explain steps. 23. > i(i + 3)²i= 1 THEOREM 4.2 Summation Formulasn(n + 1)пп1.>c = cn, c is a constant2. Si=1i=1n(n + 1)(2n + 1)6.n2(n + 1)2п3. Si?4.4i=1A proof of this theorem is given in Appendix A.CONCEPT CHECK1. Sigma NotationWhat are the index of summation,the upper bound of summation, and the lower bound ofsummation for (i – 4)?2. Sums What is the value of n?5(5 + 1)20(20 + 1)[2(20) + 1]п(a) E(b)3. Upper and Lower Sums In your own words andusing appropriate figures, describe the methods of uppersums and lower sums in approximating the area of a region.4. Finding Area by the Limit Definition Explainhow to find the area of a plane region using limits.

We expand (i+3)2 using the (a+b)2=a2+2ab+b2 formula with a=i and b=3 Then distribute i and then…

Answered: 23. > i(i + 3)² i= 1 THEOREM 4.2…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Calculus 11th Edition - Ron Larson

Chapter 4.2 - Area

"Evaluating a Sum". Use the properties of summation and Theorem 4.2 to evaluate the sum. Use the summation capabilities of a graphing utility to verify your result. Please show work and explain steps.

THEOREM 4.2 Summation Formulas
n(n + 1)
п
п
1.
>c = cn, c is a constant
2. S
i=1
i=1
n(n + 1)(2n + 1)
6.
n2(n + 1)2
п
3. Si?
4.
4
i=1
A proof of this theorem is given in Appendix A.
CONCEPT CHECK
1. Sigma Notation
What are the index of summation,
the upper bound of summation, and the lower bound of
summation for (i – 4)?
2. Sums What is the value of n?
5(5 + 1)
20(20 + 1)[2(20) + 1]
п
(a) E
(b)
3. Upper and Lower Sums In your own words and
using appropriate figures, describe the methods of upper
sums and lower sums in approximating the area of a region.
4. Finding Area by the Limit Definition Explain
how to find the area of a plane region using limits.

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