Explanation Given: The given sums are ∑ k = 0 8 1 k 2 + 1 and 2 ∑ k = 0 8 1 2 k 2 + 2 Calculation: The first sum can be written as ∑ k = 0 8 1 k 2 + 1 = 1 + 1 1 + 1 + 1 4 + 1 + 1 9 + 1 + 1 16 + 1 + 1 25 + 1 + 1 36 + 1 + 1 49 + 1 + 1 64 + 1 = 1 + 1 2 + 1 5 + 1 10 + 1 17 + 1 26 + 1 37 + 1 50 + 1 65 The second sum can be written as 2 ∑ k = 0 8 1 2 k 2 + 2 = 2 ( 1 + 1 0 + 2 + 1 2 ( 1 ) 2 + 2 + 1 2 (<

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

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Chapter 4.1, Problem 11C

To determine

To show: ∑k=081k2+1=2∑k=0812k2+2

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Chapter 4.1, Problem 10C

Chapter 4.1, Problem 12C

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∑ k = 0 8 1 k 2 + 1 = 2 ∑ k = 0 8 1 2 k 2 + 2

Solution Summary: The author explains that the first and second sums can be written as cdisplaystyle

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To show: ∑k=081k2+1=2∑k=0812k2+2

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Chapter 4 Solutions