Mathematical and Physical Journal
for High Schools
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# 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