Suppose sum_{r=0}^{2023} r cdot ^{2023}C_r = | vedclass

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(A) We use the standard identity for binomial coefficients: $\sum_{r=0}^{n} r \cdot ^{n}C_r = n \cdot 2^{n-1}$.
Given the expression $\sum_{r=0}^{202

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$1$

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(A) We use the standard identity for binomial coefficients: $\sum_{r=0}^{n} r \cdot ^{n}C_r = n \cdot 2^{n-1}$.
Given the expression $\sum_{r=0}^{2023} r \cdot ^{2023}C_r$,we substitute $n = 2023$ into the identity:
$\sum_{r=0}^{2023} r \cdot ^{2023}C_r = 2023 \cdot 2^{2023-1} = 2023 \cdot 2^{2022}$.
Comparing this result with the given expression $2023 	imes \alpha 	imes 2^{2022}$,we have:
$2023 \cdot 2^{2022} = 2023 \cdot \alpha \cdot 2^{2022}$.
Dividing both sides by $2023 \cdot 2^{2022}$,we get $\alpha = 1$.

Suppose $\sum_{r=0}^{2023} r \cdot ^{2023}C_r = 2023 \times \alpha \times 2^{2022}$. Then the value of $\alpha$ is $............$

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