Problem A. 482. (May 2009)
A. 482. Let n be a positive integer. Prove that .
(5 pont)
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
Therefore,
We proved that
which is positive.
Statistics:
4 students sent a solution. 5 points: Backhausz Tibor, Nagy 235 János, Nagy 314 Dániel, Tomon István.
Problems in Mathematics of KöMaL, May 2009