Question

1/99 - 1/99x98 - 1/98x97 - 1/97x96 - ... - 1/4x3 - 1/3x2 - 1/2x1 = ?

Answer 1

Đặt A = \(\frac{1}{99}-\frac{1}{99.98}-.....-\frac{1}{2.1}\)

\(A=\frac{1}{99}-\left[-\left(\frac{1}{1.2}+\frac{1}{2.3}+.....+\frac{1}{98.99}\right)\right]\)

\(A=\frac{1}{99}+\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-.....-\frac{1}{99}\right)\)

\(A=\frac{1}{99}+\left(1-\frac{1}{99}\right)\)

\(A=\frac{1}{99}+\frac{98}{99}=1\)