MY NOTES Lets be the sum of the series that has been shown to be convergent by the Integral Test and let ) be the function in that test. The remainder aher n temsis R s- Thus R. is the error made when the sum of the first a terms, is used an an approimation to the total sumsit can be shown that ) de s R, s n 1. Ex) d and 2. + (a) Use the sum of the first 10 terms and Equation 1 to estimate the sum of the series In (Round your answer to sx decimal places) 1549760 How good is this estimate? (b) Improve this estimate using Equation 2 with n10. (Round your answer to six decimal places.) 1.549768 (c) Find a value of n that will ensure that the error in the approximation s , is less than 0.001. n1000

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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MY NOTES
Let s be the sum of the series> an that has been shown to be convergent by the Integral Test and let x) be the function in that test. The remainder after n terms is
Thus R, is the error made when s the sum of the first n terms, is used as an approvimation to the total sum s. It can be shown that
1.
x) dx s R,s
Ex) dx
and
2. S+
(a) Use the sum of the first 10 terms and Equation 1 to estimate the sum of the series
In. (Round your answer to six decimal places.)
1.649768
How good is this estimate?
R10 s 0.1
(b) Improve this estimate using Equation 2 with n 10. (Round your answer to six decimal places.)
1.549768
(c) Find a value of n that will ensure that the error in the approximation s S, is less than 0.001.
n> 1000
Transcribed Image Text:MY NOTES Let s be the sum of the series> an that has been shown to be convergent by the Integral Test and let x) be the function in that test. The remainder after n terms is Thus R, is the error made when s the sum of the first n terms, is used as an approvimation to the total sum s. It can be shown that 1. x) dx s R,s Ex) dx and 2. S+ (a) Use the sum of the first 10 terms and Equation 1 to estimate the sum of the series In. (Round your answer to six decimal places.) 1.649768 How good is this estimate? R10 s 0.1 (b) Improve this estimate using Equation 2 with n 10. (Round your answer to six decimal places.) 1.549768 (c) Find a value of n that will ensure that the error in the approximation s S, is less than 0.001. n> 1000
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