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

  1. left parenthesis 2 straight n right parenthesis factorial
  2. text  (4n)!  end text
  3. fraction numerator left parenthesis 2 n right parenthesis factorial over denominator n end fraction
  4. n factorial

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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