9prove by induction
also use fact Sn+1 = Sn + 1/n+1
If Sn is the sum
Sn = 1 + 1/2 + 1/3 + ... 1/n ( n >2 ) ,
prove that
-
UP 0 DOWN 0 0 3
3 Answers
11@ 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).
341W/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
