Binomial (1+x)^(n+4): 5th, 6th, 7th Coefficients in AP, Find Largest Coefficient
For some n≠10, the 5th, 6th and 7th coefficients of (1+x)^(n+4) are in AP. Find n, then the largest coefficient of the expansion.
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The Remainder When 2021^2023 Is Divided by 7
Find the remainder when (2021)^2023 is divided by 7 — a modular arithmetic problem solved by reducing the base first, then finding a repeating power cycle.
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If Σr²(³⁰Cᵣ)²/(³⁰Cᵣ₋₁)=α·2²⁹ From r=1 to 30, Find α
A JEE Main 2025 binomial coefficient summation simplified by rewriting the ratio of consecutive coefficients, then splitting into two telescoping sums.