MathDB

2.3

Part of 2014 Saudi Arabia Pre-TST

Problems(1)

1/1x2, 1/2x3, 1/ 3x4, ..., 1/2013 x 2014 on a circle

Source: 2014 Saudi Arabia Pre-TST 2.3

9/13/2020
The 20132013 numbers \frac{1}{1\times 2}, \frac{1}{2\times 3},\frac{1}{3\times 4},...,\frac{1}{2013 \times 2014} are arranged randomly on a circle. (a) Prove that there exist ten consecutive numbers on the circle whose sum is less than 14000\frac{1}{4000} . (b) Prove that there exist ten consecutive numbers on the circle whose sum is less than 110000\frac{1}{10000} .
combinatorics