Question

So sánh 

\(C=1.3.5.7...99\) với \(D=\frac{51}{2}.\frac{52}{2}.\frac{53}{2}...\frac{100}{2}\)

Ai làm được giúp nha

Answer 1

Ta có:

\(D=\frac{51}{2}\cdot\frac{52}{2}\cdot\frac{53}{2}....\frac{100}{2}\)

\(=\frac{51.52.53....100}{2^{50}}\)

\(=\frac{\left(51.52.53....100\right)\left(1.2.3.....50\right)}{2^{50}\left(1.2.3.....50\right)}\)

\(=\frac{1.2.3.....100}{\left(2.1\right)\left(2.2\right)\left(2.3\right).......\left(2.50\right)}\)

\(=\frac{\left(1.3.5....99\right)\left(2.4.6....100\right)}{2.4.6....100}\)

= 1.3.5.....99 = C

Vậy C = D