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Activity 8.3.2. Consider the series While it is physically impossible to add an infinite collection of numbers, we can, of course, add any finite collection of them. In what follows, we investigate how understanding how to find the nth partial sum (that is, the sum of the first n terms) enables us to make sense of the infinite sum. a. Sum the first two numbers in this series. That is, find a numeric value for -WI “WI “WI ~WI •WI 1612 - 3 k=1 5 b. Next, add the first three numbers in the series. c. Continue adding terms in this series to complete the list below. Carry each sum to at least 8 decimal places. 1 k² k² 1 k² || || || ∞ = k² 1 2 Σ 1 k² ~WI ¬WI •W •WI =WI - -2 -2 -2 -2 || || 2 8 6 1 k=1 10 k² k=1 k² || ||

Activity 8.3.2. Consider the series While it is physically impossible to add an infinite collection of numbers, we can, of course, add any finite collection of them. In what follows, we investigate how understanding how to find the nth partial sum (that is, the sum of the first n terms) enables us to make sense of the infinite sum. a. Sum the first two numbers in this series. That is, find a numeric value for -WI “WI “WI ~WI •WI 1612 - 3 k=1 5 b. Next, add the first three numbers in the series. c. Continue adding terms in this series to complete the list below. Carry each sum to at least 8 decimal places. 1 k² k² 1 k² || || || ∞ = k² 1 2 Σ 1 k² ~WI ¬WI •W •WI =WI - -2 -2 -2 -2 || || 2 8 6 1 k=1 10 k² k=1 k² || ||

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Activity 8.3.2. Consider the series While it is physically impossible to add an infinite collection of numbers, we can, of course, add any finite collection of them. In what follows, we investigate how understanding how to find the nth partial sum (that is, the sum of the first n terms) enables us to make sense of the infinite sum. a. Sum the first two numbers in this series. That is, find a numeric value for || -WI “WI “WI “WI •WI - - - - - 22 || || k=1 k² b. Next, add the first three numbers in the series. c. Continue adding terms in this series to complete the list below. Carry each sum to at least 8 decimal places. k² k² k² k= || k² 1 2 1 k² 2 k=1 6 k=1 10 k=1 k² || 1611612 || k² || k² || ||
Transcribed Image Text:Activity 8.3.2. Consider the series While it is physically impossible to add an infinite collection of numbers, we can, of course, add any finite collection of them. In what follows, we investigate how understanding how to find the nth partial sum (that is, the sum of the first n terms) enables us to make sense of the infinite sum. a. Sum the first two numbers in this series. That is, find a numeric value for || -WI “WI “WI “WI •WI - - - - - 22 || || k=1 k² b. Next, add the first three numbers in the series. c. Continue adding terms in this series to complete the list below. Carry each sum to at least 8 decimal places. k² k² k² k= || k² 1 2 1 k² 2 k=1 6 k=1 10 k=1 k² || 1611612 || k² || k² || ||
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