Problem A. 482. (May 2009)
A. 482. Let n be a positive integer. Prove that .
Deadline expired on June 15, 2009.
Solution. Let .
The sequence is geometric sequence with quotient . In the cases =0 and =2n+1, the quitient is 1 and the last sum equals 2n+1. If 0<<2n+1, then
We proved that
which is positive.