ts] Consider the series [a, - ² Σα-Στ = 2" 3" +1 (a) Show that the series a, converges by comparing it with an appropriate geometric series b, using the comparison test. State explicitly the series b, used for comparison. n=1 n=1 (b) If we use the sum of the first k terms Σa, to approximate the sum of a, then the error #1 n=1 R₁ - Σa, will be smaller than b. Evaluate b = b as an expression in k. This serves as a 11 n=k+1 n=k+1 n=k+1 reasonable upper bound for R. (c) Using the upper bound for R, obtained in (b), determine the number of terms required to approximate the series a accurate to within 0.0003. 31 n=1
ts] Consider the series [a, - ² Σα-Στ = 2" 3" +1 (a) Show that the series a, converges by comparing it with an appropriate geometric series b, using the comparison test. State explicitly the series b, used for comparison. n=1 n=1 (b) If we use the sum of the first k terms Σa, to approximate the sum of a, then the error #1 n=1 R₁ - Σa, will be smaller than b. Evaluate b = b as an expression in k. This serves as a 11 n=k+1 n=k+1 n=k+1 reasonable upper bound for R. (c) Using the upper bound for R, obtained in (b), determine the number of terms required to approximate the series a accurate to within 0.0003. 31 n=1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![ts] Consider the series
Σα-Σ,
(a) Show that the series a, converges by comparing it with an appropriate geometric series
an
n=1
Σb, using the comparison test. State explicitly the series b, used for comparison.
n=1
n=1
(b) If we use the sum of the first k terms a to approximate the sum of a, then the error
#t=1
n=1
R = Σ a will be smaller than Σ. Evaluate Σ b as an expression in k. This serves as a
n=k+1
n=k+1
n=k+1
reasonable upper bound for R.
(c) Using the upper bound for R, obtained in (b), determine the number of terms required to
00
approximate the series a, accurate to within 0.0003.
n=1
2"](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb854e95b-6f91-4ea9-9e99-ab6ba7352139%2F1d179a9b-fcf4-4e24-9296-28c40b7a2278%2Fi26nny_processed.jpeg&w=3840&q=75)
Transcribed Image Text:ts] Consider the series
Σα-Σ,
(a) Show that the series a, converges by comparing it with an appropriate geometric series
an
n=1
Σb, using the comparison test. State explicitly the series b, used for comparison.
n=1
n=1
(b) If we use the sum of the first k terms a to approximate the sum of a, then the error
#t=1
n=1
R = Σ a will be smaller than Σ. Evaluate Σ b as an expression in k. This serves as a
n=k+1
n=k+1
n=k+1
reasonable upper bound for R.
(c) Using the upper bound for R, obtained in (b), determine the number of terms required to
00
approximate the series a, accurate to within 0.0003.
n=1
2"
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