2^n {1 cdot 3 cdot 5 cdot dots cdot (2n - 3) | vedclass

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Question

(A) We have the expression $2^n \{1 \cdot 3 \cdot 5 \cdot \dots \cdot (2n - 1)\}$.Multiply and divide by $n! = 1 \cdot 2 \cdot 3 \cdot \dots \cdot n$:

Vedclass · Accepted Answer

$\frac{(2n)!}{n!}$

Vedclass · Answer

(A) We have the expression $2^n \{1 \cdot 3 \cdot 5 \cdot \dots \cdot (2n - 1)\}$.Multiply and divide by $n! = 1 \cdot 2 \cdot 3 \cdot \dots \cdot n$:$= \frac{2^n \cdot 1 \cdot 3 \cdot 5 \cdot \dots \cdot (2n - 1) \cdot (1 \cdot 2 \cdot 3 \cdot \dots \cdot n)}{n!}$$= \frac{1 \cdot 3 \cdot 5 \cdot \dots \cdot (2n - 1) \cdot (2 \cdot 4 \cdot 6 \cdot \dots \cdot 2n)}{n!}$$= \frac{1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot \dots \cdot (2n - 1) \cdot (2n)}{n!}$$= \frac{(2n)!}{n!}$.

$2^n \{1 \cdot 3 \cdot 5 \cdot \dots \cdot (2n - 3) \cdot (2n - 1)\} = \dots$

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