Question

Cho A = 1/1.2 + 1/3.4 + 1/5.6 +...+ 1/49.50

B = 1/1 + 1/2 + 1/3 + 1/4 + ... + 1/49 + 1/50

C = 1/2 + 1/4 + 1/6 +...+1/48 + 1/50

CMR : A = B - 2C

Answer 1

A = \(\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+...+\frac{1}{49.50}\)

A = \(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{49}-\frac{1}{50}\)

A = \(\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{49}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{50}\right)\)

A = \(\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{49}+\frac{1}{50}\right)-2.\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{50}\right)\)

A = B - 2C ( ĐPCM )

Vậy A = B - 2C