The sequence a(1),a(2),a(3),..., is formed according to the recursive rule a(1)=1, a(2)=a(1)+1/a(1),..., a(n+1)=a(n)+1/a(n), ...
Prove that a(100) > 14.

No direct evaluation, of course.

(In reply to Solution(Correction) by John Dounis)

Bravo!

Excellent reasoning.

You did not need to post twice- 1.messy and then 2.corrected

You are free to edit your post , even several times.

Welcome to FLOOBLES - you will not be a novice for long....

 

Posted by Ady TZIDON on 2011-12-06 16:27:44