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JEE Main202324 Jan 2023Morning ShiftMathematicsBinomial TheoremActual

Suppose ∑ r = 0 2023 r 2 · C r 2023 = 2023 × α × 2 2022 , then the value of α is

Correct answer

0

Step-by-step solution

Given, ∑ r = 0 2023 r 2 · C r 2023 = 2023 × α × 2 2022 Now taking L.H.S we get, ∑ r = 0 2023 r 2 · C r 2023 = ∑ r = 1 2023 r 2 · 2023 r · C r - 1 2022 ⇒ ∑ r = 0 2023 r 2 · C r 2023 = ∑ r = 1 2023 r · 2023 · C r - 1 2022 ⇒ ∑ r = 0 2023 r 2 · C r 2023 = 2023 ∑ r = 1 2023 r - 1 + 1 · C r - 1 2022 ⇒ ∑ r = 0 2023 r 2 · C r 2023 = 2023 ∑ r = 1 2023 r - 1 · C r - 1 2022 + ∑ r

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