Question

a,  Tìm STN x, biết: 2+4+6+...+2x=210

b, Cho A= 1x3x5x7x...x99

          B=51/2 x 52/2 x 53/2 x...x 100/2

Chứng tỏ A=B ?

Answer 1

a, 2 + 4 + 6 +...+ 2x = 210

=> 2(1 + 2 + 3 +...+ x) = 210

=> \(\frac{2x\left(x+1\right)}{2}=210\)

=> x(x + 1) = 210

=> x(x + 1) = 14.15

=> x = 14

b, Ta có: \(B=\frac{51}{2}.\frac{52}{2}.\frac{53}{2}....\frac{100}{2}=\frac{51.52.53....100}{2^{50}}\)

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

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

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

\(=1.3.5.....99=B\)

Vậy A = B