JEE Advanced: Nested Sum Collapses With One Elegant Idea! скачать в хорошем качестве

JEE Advanced: Nested Sum Collapses With One Elegant Idea!

JEE Advanced: Nested Sum Collapses With One Elegant Idea! | Factorial's Question of the Day In this video from Factorial’s Question of the Day, we take a seemingly complicated nested sum with binomial coefficients and convert it into a beautiful integral expression that collapses the entire problem in just a few steps. This is one of those problems that looks intimidating at first, but becomes incredibly elegant once you use the right identity: If p = ∑_{r=1}^{50} { ∑_{k=1}^{r} [ (-1)^{r-1} / k ] } · 50C_r, then find the value of 200p. This single observation transforms the entire inner sum into a closed form, and with one binomial identity, the complete expression melts into a simple integral. Students will absolutely love this approach — it’s clean, powerful, and deeply satisfying. 📌 Concepts Used Converting sums to integrals Binomial expansion tricks Swapping summations Classic alternating sum identity Beautiful collapse into a simple definite integral 🎯 Series: Factorial’s Question of the Day — JEE Advanced 2026 📲 Join the Telegram community for revision notes & updates: https://t.me/academyfactorial #JEE2026 #JEEMaths2026 #JEEMains2026 #JEEAdvanced #JEEAdvanced2026 #IITJEE #BinomialTheorem #DefiniteIntegration #IntegralTrick #FactorialAcademy #QOTD #RankerConcept