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Question 2
Let an = Hn - ln(n), where Hn is the nth harmonic number
Hn = 1 + 1/2 + .... + 1/n
a. Show that an > 0 for n>= 1 (Hint: show Hn >= integral from 1 to n+1 dx/x)
b. Show {an} is decreasing by interpreting an - an+1 as a positive area. (Hint: use the previous part)
c. Prove lim n-> infinity an exists
Let an = Hn - ln(n), where Hn is the nth harmonic number
Hn = 1 + 1/2 + .... + 1/n
a. Show that an > 0 for n>= 1 (Hint: show Hn >= integral from 1 to n+1 dx/x)
b. Show {an} is decreasing by interpreting an - an+1 as a positive area. (Hint: use the previous part)
c. Prove lim n-> infinity an exists
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