The value of (1/1 !(n-1) !)+(1/3 !(n-3))+(1/5 !(n-5) !)+ ldots ldots .. is

Question

The value of (1/1 !(n-1) !)+(1/3 !(n-3))+(1/5 !(n-5) !)+ ldots ldots .. is (A) (2n/(n-1) !) (B) (2n/n !) (C) (2n-1/(n-1) !) (D) (2n-1/n !)

Tardigrade Admin · Accepted Answer

Let S=(1/1 !(n-1) !)+(1/3 !(n-3))+(1/5 !(n-5) !)+ ldots ldots =(1/n !)((n !/1 !(n-1) !)+(n !/3 !(n-3) !)+(1/5 !(n-5) !)+ ldots ..) =(1/n !)( n C1+ n C3+ n C5+ ldots ldots) =(1/n !) ⋅ (2n/2) ⇒ (2n-1/n !)

Q. The value of $\frac{1}{1 ! ( n - 1 )!} + \frac{1}{3 ! ( n - 3 )} + \frac{1}{5 ! ( n - 5 )!} + \dots\dots .$ . is

$\frac{2 ^{n}}{( n - 1 )!}$

$\frac{2 ^{n}}{n !}$

$\frac{2 ^{n - 1}}{( n - 1 )!}$

$\frac{2 ^{n - 1}}{n !}$

Q. The value of 1!(n−1)!1​+3!(n−3)1​+5!(n−5)!1​+…….. is

(n−1)!2n​

n!2n​

(n−1)!2n−1​

n!2n−1​

Let S=1!(n−1)!1​+3!(n−3)1​+5!(n−5)!1​+…… =n!1​(1!(n−1)!n!​+3!(n−3)!n!​+5!(n−5)!1​+…..) =n!1​(nC1​+nC3​+nC5​+……) =n!1​⋅22n​⇒n!2n−1​

Q. The value of $\frac{1}{1 ! ( n - 1 )!} + \frac{1}{3 ! ( n - 3 )} + \frac{1}{5 ! ( n - 5 )!} + \dots\dots .$ . is

$\frac{2 ^{n}}{( n - 1 )!}$

$\frac{2 ^{n}}{n !}$

$\frac{2 ^{n - 1}}{( n - 1 )!}$

$\frac{2 ^{n - 1}}{n !}$