Estimate the series n= n to within an accuracy of 0.5. Hint: Find an upper bound on the remainders of partial sums of the series. One method begins by recalling that for n ≥ 1. n² 2 < (²/1-1²-₁1) ; n n+1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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mathematics

Estimate the series
∞ 1
n
to within an accuracy of 0.5.
n=1
Hint: Find an upper bound on the remainders of partial sums of the series.
One method begins by recalling that
for n ≥ 1.
1
2
; ≤ ( ²1 - ²4/1)
n+1
n²
Transcribed Image Text:Estimate the series ∞ 1 n to within an accuracy of 0.5. n=1 Hint: Find an upper bound on the remainders of partial sums of the series. One method begins by recalling that for n ≥ 1. 1 2 ; ≤ ( ²1 - ²4/1) n+1 n²
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