Question

(n+1) x (n+2) x (n+3) .... ( 2xn) chia hết cho 2 mũ n

Answer 1

\(\left(n+1\right)\left(n+2\right)...\left(2n\right)=\frac{1.2.3.....n.\left(n+1\right)\left(n+2\right)...\left(2n\right)}{1.2.3.....n}\)

\(=\frac{1.3.5.....\left(2n-1\right).2.4.6.....\left(2n\right)}{1.2.3.....n}=\frac{1.3.5.....\left(2n-1\right).2^n\left(1.2.3.....n\right)}{1.2.3.....n}\)

\(=1.3.5.....\left(2n-1\right).2^n⋮2^n\).