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MathsHardNumerical2023 ยท 24 Jan Shift 1

Q85.Suppose โˆ‘๐‘Ÿ=20230 ๐‘Ÿ2 ยท 2023๐ถ๐‘Ÿ= 2023 ร— ๐›ผร— 22022, then the value of ๐›ผ is

What This Question Tests

This question is a advanced problem on binomial series, requiring knowledge of identities involving sums of r*nCr and r^2*nCr, which are typically derived by differentiating the binomial expansion of (1+x)^n.

Concepts Tested

Binomial coefficientsDifferentiation of binomial expansionSummation properties

Formulas Used

(1+x)^n = ฮฃ nCr x^r

ฮฃ r nCr x^r = nx(1+x)^(n-1)

ฮฃ r^2 nCr x^r = n(n-1)x^2(1+x)^(n-2) + nx(1+x)^(n-1)

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