23. > i(i + 3)² i= 1 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.
23. > i(i + 3)² i= 1 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.
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter1: Introduction To Algebra
Section1.4: Translating Words Into Symbols
Problem 8MRE
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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.
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