6

Part of 2012 Hanoi Open Mathematics Competitions

Problems(2)

Q6 - Hanoi Open Mathematical Olympiad 2012 - Junior Section

Source:

3:00

AM, the temperature was

13^o

below zero. By none it has risen to

32^o

. What is the average hourly increase in temperature ?

Source:

For every n = 2; 3; : : : , we put

A_n = \left(1 - \frac{1}{1+2}\right) X \left(1 - \frac{1}{1+2+3}\right)X \left(1 - \frac{1}{1+2+3+...+n}\right)

Determine all positive integer n (n \geq 2) such that

\frac{1}{A_n}