1-n-n-n-1-2-n-n-1-n-2-3-n-n-1-n-2-n-3-4-

Question Number 37728 by kunal1234523 last updated on 17/Jun/18

1 + n + \frac{n (n - 1)}{2!} + \frac{n (n - 1) (n - 2)}{3!} + \frac{n (n - 1) (n - 2) (n - 3)}{4!} + \dots \dots . . =

Answered by tanmay.chaudhury50@gmail.com last updated on 17/Jun/18

{(1 + x)}^{n} = 1 + {n C}_{1} x + {n C}_{2} x^{2} + {n C}_{3} x^{3} + \dots + {n C}_{n} x^{n}

p u t x = 1

2^{n} = 1 + {n C}_{1} + {n C}_{2} + {n C}_{3} + \dots + {n C}_{n}

2^{n} = 1 + n + \frac{n (n - 1)}{2!} + \frac{n (n - 1) (n - 2)}{3!}

s o t h e a n s w e r i s 2^{n}

Commented by kunal1234523 last updated on 17/Jun/18

Commented by kunal1234523 last updated on 17/Jun/18

according to wolfram alpha it can not be

determine in general form but you did it

are you a genius

Commented by kunal1234523 last updated on 17/Jun/18

This question is arived to me when I am

working on sets . I came to know that no . of

subsets of a set is 2^{n} where n is no . of terms

or objects in the set . so I tried to prove it and

I end up in the question that I had asked .