We know that the remainder R, will satisfy |Rn| s bn + 1 : (n + 1)9" + 1' We must make n large enough so that this is less than 0.0001. Rounding to five decimal places, we have b2 = b3 = and b4 = Submit Skip (you cannot come back)

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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Test the series for convergence or divergence. If the series is convergent, use the Alternating Series
Estimation Theorem to determine how many terms we need to add in order to find the sum with an error less
than 0.0001?
5(-1)"
ngn
n = 1
Step 1
The terms of the series ) decrease as n → o and
ngn
lim
n+ o ngn
n = 1
Step 2
(-1)"
is convergent
convergent
Therefore, by the Alternating Series Test,
ngn
n = 1
Step 3
1
We know that the remainder Rn will satisfy |Rnl s bn + 1 =
(n + 1)9n + 1'
We must make n large enough so that this is less than 0.0001.
Rounding to five decimal places, we have b2 =
b3
and
b4 =
Submit
Skip (you cannot come back)
Transcribed Image Text:Test the series for convergence or divergence. If the series is convergent, use the Alternating Series Estimation Theorem to determine how many terms we need to add in order to find the sum with an error less than 0.0001? 5(-1)" ngn n = 1 Step 1 The terms of the series ) decrease as n → o and ngn lim n+ o ngn n = 1 Step 2 (-1)" is convergent convergent Therefore, by the Alternating Series Test, ngn n = 1 Step 3 1 We know that the remainder Rn will satisfy |Rnl s bn + 1 = (n + 1)9n + 1' We must make n large enough so that this is less than 0.0001. Rounding to five decimal places, we have b2 = b3 and b4 = Submit Skip (you cannot come back)
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