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.
Q.1 Which of the following is equal to $latex 1 + \frac{1}{1+\frac{1}{1+1}}$?
Answer of (Q.2) This solution is using hints.
If we pair up the elements of $latex X$ it will look like $latex (10,100)(12,98),(14,96),.....(54,56)$. Now sum of the each pair is $latex 110$. Number of pair $latex =\frac{Number of terms}{2} =\frac{46}{2}$. so $latex X$ will be equal to Number of pair $latex \times 110 =\frac{46}{2} \times 110=2530$ , similarly $latex Y$ will be $latex \frac{46}{2} \times 114=2622$.
So, $latex Y-X$ will be $latex 92$.
Q.1 Find all positive integers $latex n$ such that $latex n^2+1$ is divisible by $latex n+1$.
Also Visit: Cheenta Olympiad Program
Q.2 Two geometric sequences $latex a_1, a_2, a_3, \ldots$ and $latex b_1, b_2, b_3, \ldots$ have the same common ratio, with $latex a_1 = 27$, $latex b_1=99$, and $latex a_{15}=b_{11}$. Find $latex a_9$.
Example of Geometric Sequence $latex 2,4,8,16$, here common ratio is $latex 2$.
Q.1 Let $latex m$, $latex n$, $latex p$ be real numbers such that $latex m^2 + n^2 + p^2 - 2mnp = 1$ . Prove that $latex (1+m)(1+n)(1+p) \leq 4 + 4mnp$.
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's M.Stat Entrance. They ranked within the first 50 in the entire country in these entrances. I.S.I. M.Stat Entrance
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Cheenta Academy proudly celebrates the success of 27 current and former students who qualified for the Indian Olympiad Qualifier in Mathematics (IOQM) 2025, advancing to the next stage — RMO. This accomplishment highlights their perseverance and Cheenta’s ongoing mission to nurture mathematical excellence and research-oriented learning.
