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JEE Main20257 Apr 2025Evening ShiftMathematicsBinomial TheoremActual

The sum of the series 2 1 ²⁰ C ₄-3 2 ²⁰ C ₅+4 3 ²⁰ C ₆-5 4 ²⁰ C ₇+ +18 17 ²⁰ C ₂₀ , is equal to

Correct answer

0

Step-by-step solution

aligned & (1- x )²⁰= ²⁰ C ₀- ²⁰ C ₁ x + ²⁰ C ₂ x ^2 . .+ ²⁰ C ₂₀ x ²⁰ & (1- x )²⁰ x ^2 = ²⁰ C ₀ x ^2 - ²⁰ C ₁ x + ²⁰ C ₂- ²⁰ C ₃ x + ²⁰ C ₄ x ^2 aligned Diff twice and put x =1 aligned & =6- ²⁰ C ₁(2)+ A & ~A =40-6=34 aligned

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