The highest power of 2 in 10! + 11! + 12! + 13! + ...+ 1000! is
(a) 8
(b) 9
(c) 10
(d) 11
We can write the given expression in the following form
10! + 11*10! + 12*11*10! + 13*12*11*10! + ...
= 10!(1 + 11 + 11× 12 + ....)
= 10!(12 + 11× 12 + ....)
= 10! (12)(1 + 11 + .....).
This contain 8 + 2 = 10 number of 2's.
