Question

Thực hiện phép tính :        1/99x97 - 1/97x95 - 1/95x93 - ... - 1/5x3 - 1/3x1

Answer 1

Đặt A =\(\frac{1}{99x97}+\frac{1}{97x95}+...+\frac{1}{3x1}\)

2A =\(\frac{2}{99x97}+\frac{2}{97x95}+...+\frac{2}{3x1}\)

2A=\(\frac{1}{97}-\frac{1}{99}+\frac{1}{95}-\frac{1}{97}+...+\frac{1}{1}-\frac{1}{3}\)

2A=1-\(\frac{1}{99}\)=\(\frac{98}{99}\)

=> A=\(\frac{49}{99}\)