Explanation Given information: The sum is given by ∑ k = 1 4 ( ( 2 + k ) 2 + 1 ) . Calculation: First write the sum of all numbers of the form ( ( 2 + k ) 2 + 1 ) , k = 1 , 2 , 3 , 4 Then add all of these values, ∑ k = 1 4 ( ( 2 + k ) 2 + 1 ) = ( ( 2 + 1 ) 2 + 1 ) + ( ( 2 + 2 ) 2 + 1 ) + ( ( 2 + 3 ) 2 + 1 ) + ( ( 2 + 4 ) 2 + 1 )

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 4.1, Problem 34S

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To calculate: Expand the sum and determine the value of the sum.

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Chapter 4.1, Problem 33S

Chapter 4.1, Problem 35S

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Expand the sum and determine the value of the sum.

Solution Summary: The author explains how to calculate the sum of all numbers of the form (2+k)2+1 ).

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Chapter 4 Solutions