Problem Solving Marathon Week1 Solution is the effortless attempt from Cheenta’s existing student as well as from the end of mentor. Question, rules and hints are given here.

## Level 0

**Q.1** Which of the following is equal to ?

This solution is proposed by Swetaabh Mishra from Thousand Flowers.

**Answer of (Q.2) ** This solution is using hints.

If we pair up the elements of it will look like

So,

## Level 1

**Q.1** Find all positive integers

Since,

We can say that if

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**Q.2** Two geometric sequences

Example of Geometric Sequence

This solution is proposed by Saikrish Kailash from Thousand Flowers.

Two geometric sequence have same common ratio, let it is

Now

## Level 2

**Q.1** Let

This solution is proposed by Sampreety Pillai from Early Bird Math Olypmiad Group.

We konw

So

Also you can do another type of proof using Cauchy-Schwarz inequality. For that click here.