INEQUALITIES :(


If Sn is the sum

Sn = 1 + 1/2 + 1/3 + ... 1/n ( n >2 ) ,

prove that

3 Answers

9
Celestine preetham ·

prove by induction

also use fact Sn+1 = Sn + 1/n+1

11
Devil ·

@ Cele, I'd really like to know how exactrly we use induction when the variable assumes values >1...(As in this case)....
(This problem, of using induction has been killing me since ages....I'd be really gr8ful if u show it).

341
Hari Shankar ·

W/o induction (seems easier to me)

(1+1) + \left(1 + \frac{1}{2} \right) +...+\left(1 + \frac{1}{n} \right) \ge n \sqrt [n] { 2 \times \frac{3}{2} \times...\times \frac{n+1}{n} } = n \sqrt [n] {(n+1)}

\Rightarrow S_n > \sqrt [n] {n+1} - n

The left inequality can be finished in the same way

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