olymmath

TM-MO 2015

Turkmenistan national mathematics olympiad 2015.

Other problems

Problem 2

Find lim⁡n→∞(∑i=0n1n+i)\lim_{n\to\infty}(\sum_{i=0}^{n}\frac{1}{n+i})

Problem 3

Find the sum : C1nC^{n}_{1} - 13⋅C3n\frac{1}{3} \cdot C^{n}_{3} + 19⋅C5n\frac{1}{9} \cdot C^{n}_{5} - 127⋅C9n\frac{1}{27} \cdot C^{n}_{9} + ...

Problem 4

Find the max and minimum without using dervivate: x+4⋅12−x\sqrt{x} +4 \cdot \sqrt{\frac{1}{2} - x}