Question

CM : \(1.3.5.....99=\frac{51}{2}.\frac{52}{2}.....\frac{100}{2}\)

Answer 1

\(1.3.5....99=\frac{1.2.3.4....99.100}{2.4.6...100}=\frac{\left(1.2.3....50\right).\left(51.52.53...100\right)}{2^{50}.\left(1.2.3...50\right)}\)

\(=\frac{51.52.53....100}{2^{50}}=\frac{51}{2}.\frac{52}{2}.\frac{53}{2}......\frac{100}{2}\)

Answer 2

Ta có :

\(1.3.5.....99=\frac{1.2.3.4.....99.100}{2.4.6......100}\)

\(=\frac{1.2.3......99.100}{1.2.2.2.2.3......2.50}\)

\(=\frac{1.2.3.4......99.100}{2^{50}.1.2.3......50}\)

\(=\frac{51.52.....100}{2^{50}}\)

\(=\frac{51}{2}.\frac{52}{2}...........\frac{100}{2}\) (ĐPCM)