00 Consider the series S= Σ A-2 1 m (Inn)5 and let S = 1 (Inn) For each integer N > 2, let RS-Sy. Recall that for all N>2, the precise version of the Integral Test gives dz S N+1 2(Inx)³ = Ry≤ a) Find the smallest integer N> 2 for which the second inequality in line (+) gives RN <0.009. ANSWER: N = b) Use the value of N from part (a) to fill in precise decimal values in the following analogue of line (*): (22) #SRNS dz IN z(Inz) c) Continue with the N found in part (a). Without further information, the best approximation for R is Ry, the midpoint of the interval in line (**). Use this to find an accurate pproximation for the sum S. ANSWER: S SN + RN =
00 Consider the series S= Σ A-2 1 m (Inn)5 and let S = 1 (Inn) For each integer N > 2, let RS-Sy. Recall that for all N>2, the precise version of the Integral Test gives dz S N+1 2(Inx)³ = Ry≤ a) Find the smallest integer N> 2 for which the second inequality in line (+) gives RN <0.009. ANSWER: N = b) Use the value of N from part (a) to fill in precise decimal values in the following analogue of line (*): (22) #SRNS dz IN z(Inz) c) Continue with the N found in part (a). Without further information, the best approximation for R is Ry, the midpoint of the interval in line (**). Use this to find an accurate pproximation for the sum S. ANSWER: S SN + RN =
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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Transcribed Image Text:Consider the series S=
00
1
(Inn)5¹
and lot Sw=
N
R-2
1
n(Inn)
For each integer N≥ 2, let Ry = S- Sy. Recall that for all N> 2, the precise version of the Integral Test gives
dz
√N FSRN S
(a) Find the smallest integer N> 2 for which the second inequality in line (*) gives RN < 0.009.
ANSWER: N=
(b) Use the value of N from part (a) to fill in precise decimal values in the following analogue of line (*):
≤RN S
< Writers
(c) Continue with the N found in part (a). Without further information, the best approximation for Ry is Ry, the midpoint of the interval in line (**). Use this to find an accurate
approximation for the sum S.
ANSWER: S SN + RN =
#
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