Question

Show that (2) ^16 divides 32! . Find highest power of 2 that divides 32!

Answer 1

Answer:

taking n(n+1)/6 common, we get

1/2 [ 2{n(n+1)/2}^2 – n(n+1)(2n+1)/6 + n(n+1)/2]=[3n(n+1) – (2n+1)+3]*n(n+1)/12

=[3n^2+3n – 2n – 1+3]*n(n+1)/12

=1/12 [ n(n+1) {3(n^2) + n +2}]