Combi-Spanish olympiad_1985

[Md Ashraful Kader]

please help me to solve this prob:
"prove that for each n,where n is real number,
(n+1)(n+2)...(2n) is divisible by 2^n

[nahin munkar]

It's easy to prove by induction.after base case, let ,2^n divides (n+1).....(2n).(inductive hypothesis). Then,simply prove 2^(n+1) or,(2^n)*2 divides{(n+2).(n+3)....(2n).2(n+1)}. You can see easily,(2^n)*2 divides {2.(n+1).(n+2).......(2n)}[from inductive hypothesis] .So,(n+1)(n+2)...(2n) is divisible by 2^n. [proved]

[SMMamun]

Are you certain that n is a real number, not an integer? n as a real number will make the problem uninteresting.

Consider n an integer, and apply the Method of Mathematical Induction (গাণিতিক আরোহ পদ্ধতি).