The value of {2^n} { 1 cdot 3 cdot 5 cdots (2 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) We have the expression $E = {2^n} \{ 1 \cdot 3 \cdot 5 \cdots (2n - 1) \}$.To simplify this,multiply and divide by the product of even numbers $2

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) We have the expression $E = {2^n} \{ 1 \cdot 3 \cdot 5 \cdots (2n - 1) \}$.To simplify this,multiply and divide by the product of even numbers $2 \cdot 4 \cdot 6 \cdots (2n)$:$E = \frac{{2^n} \{ 1 \cdot 3 \cdot 5 \cdots (2n - 1) \} \cdot \{ 2 \cdot 4 \cdot 6 \cdots (2n) \}}{2 \cdot 4 \cdot 6 \cdots (2n)}$$E = \frac{(2n)!}{2 \cdot 1 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdots 2 \cdot n}$$E = \frac{(2n)!}{{2^n} \cdot (1 \cdot 2 \cdot 3 \cdots n)}$$E = \frac{(2n)!}{{2^n} \cdot n!} \cdot {2^n} = \frac{(2n)!}{n!}$.

The value of ${2^n} \{ 1 \cdot 3 \cdot 5 \cdots (2n - 3) \cdot (2n - 1) \}$ is

Similar Questions

Five-digit numbers are formed using the digits $1, 2, 3, 5, 7$ with repetitions and are written in descending order with serial numbers. For example,the number $77777$ has serial number $1$. Then the serial number of $35337$ is $.........$.

The number of $4$-digit numbers that can be formed from the digits $0, 1, 2, 3, 4, 5, 6, 7$ such that each number contains the digit $1$ is:

The number of different words that can be formed from the letters of the word "$INTERMEDIATE$" such that two vowels never come together,is

The number of positive integral solutions of $xyz = 60$ is

The sum of all the $4$-digit numbers formed by taking all the digits from ${0, 3, 6, 9}$ without repetition is

Vedclass Test Series

Exam Paper Generator

Online Exam Module