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Maths-

General

Easy

Question

The value of $2 to the power of n n factorial$ $left parenthesis 1.3.5 horizontal ellipsis left parenthesis 2 n minus 1 right parenthesis right parenthesis$ is

$(2 n)!$
$(4n)!$
$\frac{(2 n)!}{n}$
$n!$

hint Hint:

In the question we will need to know the pattern for this we will put different values of n one by one. Then we will observe the pattern to know the answer.

The correct answer is: $left parenthesis 2 straight n right parenthesis factorial$

let P = $2 to the power of n n factorial$ $left parenthesis 1.3.5 horizontal ellipsis left parenthesis 2 n minus 1 right parenthesis right parenthesis$
let n=1, then $2 to the power of 1.1 factorial space.1 space equals 2.1 space equals 2 factorial$
let n=2, then, $2 squared.2 factorial. left parenthesis 1. left parenthesis 2.2 minus 1 right parenthesis right parenthesis equals 4.2.1.3 equals 4 factorial$
let n=3, then, $2 cubed. space 3 factorial. space left parenthesis 1.3. left parenthesis 2.2 minus 1 right parenthesis right parenthesis equals 2.2.2.3 factorial. left parenthesis 1.3.5 right parenthesis equals 3 factorial.4.5.6 equals 6 factorial$
Now looking at the pattern we can say that
when n=1, P=(2.1)!
when n=2, P =(2.2)!
when n=3 P= (2.3)!
So, P =(2n)!

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