Problems – We Solve Problem
Filter Problems
Showing 1 to 20 of 22 entries

Counting in two ways , Exponential functions and logarithms (other) , Integer and fractional parts. Archimedean property

Prove that for every natural number n $>$ 1 the equality: [$n^{1 / 2}] + [n^{1/ 3}] + … + [n^{1 / n}] = [log_{2}n] + [log_{3}n] + … + [log_{n}n]$ is satisfied.

Algebraic inequalities (other) , Counting in two ways , Integer and fractional parts. Archimedean property

Prove that for any positive integer n the inequality is true.

Counting in two ways , Partitions into pairs and groups bijections , Pigeonhole principle (other)

You are given 25 numbers. The sum of any 4 of these numbers is positive. Prove that the sum of all 25 numbers is also positive.

My Problem Set reset
No Problems selected