Precalculus with Limits: A Graphing Approach
7th Edition
ISBN: 9781305071711
Author: Ron Larson
Publisher: Brooks/Cole
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Question
Chapter 8.1, Problem 108E
To determine
To write: the sum under sigma notation and evaluate it by graphing utility.
Expert Solution & Answer
Answer to Problem 108E
The sum can be written as 7∑j=0(−1)j(12)j .
And
7∑j=0(−1)j(12)j=85128
Explanation of Solution
Given information:
A finite series expression is given as
1−12+14−18+...−1128
Concept used:
A finite series of the form a1+a2+a3+...+an can be written in sigma notation as
n∑j=1aj
Calculation:
Consider the series expression.
1−12+14−18+...−1128
Here, the series can be rewritten as
(−1)0(12)0+(−1)1(12)1+(−1)2(12)2+(−1)3(12)3+...+(−1)7(12)7
So, the lower index is 0 and upper index is 7.
Consider the variable j to write the index lower limit and upper limit for the sum.
So, the series can be written in sigma notation as
(−1)0(12)0+(−1)1(12)1+(−1)2(12)2+(−1)3(12)3+...+(−1)7(12)7=7∑j=0(−1)j(12)j
Follow the below steps to evaluate the sum by graphing utility
- Choose the SUM feature from MATH menu
- Choose SEQUENCE feature from OPERATION menu
- Enter the expression for the sequence (−1)j(12)j , variable of the sequence (j) , lower limit of the summation (0) , upper limit of the summation (7)
- Press the button ENTER
The calculator will display the result as 85128 .
Hence, the value of the sum is
7∑j=1(−1)j(12)j=85128
Chapter 8 Solutions
Precalculus with Limits: A Graphing Approach
Ch. 8.1 - Prob. 1ECh. 8.1 - Prob. 2ECh. 8.1 - Prob. 3ECh. 8.1 - Prob. 4ECh. 8.1 - Prob. 5ECh. 8.1 - Prob. 6ECh. 8.1 - Prob. 7ECh. 8.1 - Prob. 8ECh. 8.1 - Prob. 9ECh. 8.1 - Prob. 10E
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Prob. 81RECh. 8 - Prob. 82RECh. 8 - Prob. 83RECh. 8 - Prob. 84RECh. 8 - Prob. 85RECh. 8 - Prob. 86RECh. 8 - Prob. 87RECh. 8 - Prob. 88RECh. 8 - Prob. 89RECh. 8 - Prob. 90RECh. 8 - Prob. 91RECh. 8 - Prob. 92RECh. 8 - Prob. 93RECh. 8 - Prob. 94RECh. 8 - Prob. 95RECh. 8 - Prob. 96RECh. 8 - Prob. 97RECh. 8 - Prob. 98RECh. 8 - Prob. 99RECh. 8 - Prob. 1CTCh. 8 - Prob. 2CTCh. 8 - Prob. 3CTCh. 8 - Prob. 4CTCh. 8 - Prob. 5CTCh. 8 - Prob. 6CTCh. 8 - Prob. 7CTCh. 8 - Prob. 8CTCh. 8 - Prob. 9CTCh. 8 - Prob. 10CTCh. 8 - Prob. 11CTCh. 8 - Prob. 12CTCh. 8 - Prob. 13CTCh. 8 - Prob. 14CTCh. 8 - Prob. 15CTCh. 8 - Prob. 16CTCh. 8 - Prob. 17CTCh. 8 - Prob. 18CTCh. 8 - Prob. 19CTCh. 8 - Prob. 20CTCh. 8 - Prob. 21CTCh. 8 - Prob. 22CTCh. 8 - Prob. 23CTCh. 8 - Prob. 24CTCh. 8 - Prob. 25CTCh. 8 - Prob. 26CT
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