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We know that the harmonic series has a growth rate comparable to In n. Let an = 1/2 and defin a new sequence (tn) by tn = Sn - Inn 1 = 1+ + 2 1 n In n Prove that (tn) is a positive, monotone-down sequence, which therefore converges.32

We know that the harmonic series has a growth rate comparable to In n. Let an = 1/2 and defin a new sequence (tn) by tn = Sn - Inn 1 = 1+ + 2 1 n In n Prove that (tn) is a positive, monotone-down sequence, which therefore converges.32

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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n We know that the harmonic series has a growth rate comparable to In n. Let an = 1/2 and define a new sequence (tn) by tn = Sn - Inn = 1+ 1 2 + 1 n - In n Prove that (tn) is a positive, monotone-down sequence, which therefore converges. (Hint: you'll need the mean value theorem from elementary calculus)
Transcribed Image Text:n We know that the harmonic series has a growth rate comparable to In n. Let an = 1/2 and define a new sequence (tn) by tn = Sn - Inn = 1+ 1 2 + 1 n - In n Prove that (tn) is a positive, monotone-down sequence, which therefore converges. (Hint: you'll need the mean value theorem from elementary calculus)
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