PYMT #27 | An Elegant Limit Every JEE Aspirant Should Know ⭐⭐⭐⭐⭐ #jeeadvanced

Welcome to PYMT #27 (Problems You Must Try) Today's problem is a beautiful blend of Trigonometry and Limits, taken from JEE Advanced Study Material. At first glance, the expression looks intimidating. It involves an infinite product, a trigonometric function, and a limit: [ T_k=\prod_{n=2}^{k}\left(1-4\sin^2\frac{\pi}{3\cdot2^n}\right) ] The challenge is to evaluate [ \lim_{k\to\infty}\frac{4}{T_k}. ] Many students instinctively begin expanding terms or applying approximations. But this problem is designed to reward a completely different approach. A single observation transforms the entire expression into a beautiful telescoping product, making the solution elegant, concise, and deeply satisfying. If you're preparing for JEE Advanced or simply enjoy discovering beautiful mathematics, this is a problem you shouldn't miss. Source: JEE Advanced Study Material If you enjoyed this problem, don't forget to Like, Share, and Subscribe for more episodes of PYMT – Problems You Must Try, where we explore problems that are not just challenging, but genuinely beautiful. #PYMT #Limits #Calculus #Trigonometry #JEEAdvanced #Mathematics #ProblemSolving #StayMathactive