Question

Show that 2^n-n/1!.2^(n-1)+n(n-1)/2!.2^(n-2)-.....+(-1)^n=1?

Answer 1

See below.

Explanation:

`(2-1)^n = 2^n-n/(1!)2^(n-1)+(n(n-1))/(2!)2^(n-2)+cdots+(-1)^n = 1`