Suppose displaystyle∑r=02023 r22023 Cr=2023 × α × 22022. Then the value of α is

Question

Suppose displaystyle∑r=02023 r22023 Cr=2023 × α × 22022. Then the value of α is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

using result displaystyle∑ r =0 n r 2 n C r = n ( n +1) ⋅ 2 n -2 Then displaystyle∑ r =02023 r 2 2023 C r =2023 × 2024 × 22021 =2023 × α × 22022 text So, ⇒ α=1012

Q. Suppose $r = 0 \sum 2023 r^{22023} C_{r} = 2023 \times α \times 2^{2022}$ . Then the value of $α$ is

using result
$r = 0 \sum n r^{2}^{n} C_{r} = n (n + 1) \cdot 2^{n - 2}$
Then $r = 0 \sum 2023 r^{2}^{2023} C_{r} = 2023 \times 2024 \times 2^{2021}$
$= 2023 \times α \times 2^{2022} So,$
$\Rightarrow α = 1012$

Q. Suppose r=0∑2023​r22023Cr​=2023×α×22022. Then the value of α is

using result r=0∑n​r2nCr​=n(n+1)⋅2n−2 Then r=0∑2023​r22023Cr​=2023×2024×22021 =2023×α×22022 So, ⇒α=1012

Q. Suppose $r = 0 \sum 2023 r^{22023} C_{r} = 2023 \times α \times 2^{2022}$ . Then the value of $α$ is

using result
$r = 0 \sum n r^{2}^{n} C_{r} = n (n + 1) \cdot 2^{n - 2}$
Then $r = 0 \sum 2023 r^{2}^{2023} C_{r} = 2023 \times 2024 \times 2^{2021}$
$= 2023 \times α \times 2^{2022} So,$
$\Rightarrow α = 1012$