Analysis nWe know that the harmonic series has a growth rate comparable to In n. Let an = 1/2 and definea new sequence (tn) bytn=Sn-Inn = 1+12+1n- In nProve that (tn) is a positive, monotone-down sequence, which therefore converges.(Hint: you'll need the mean value theorem from elementary calculus)

Now, let’s consider the sequence (tn) defined by tn=sn−lnn=1+1/2+…−1/n−ln(n), where s_n is the nth…

Answered: We know that the harmonic series has a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Frequency 300- 200- 100- 0- Employee Salaries 32 37 42 47 52 57 62 Salary (in thousands of dollars)
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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