Question

Tính \(A=\dfrac{1+\left(1+2\right)+...+\left(1+2+...+98\right)}{1.2+2.3+...+98.99}\)

Answer 1

\(A=\dfrac{1+\left(1+2\right)+\left(1+2+3\right)+.........+\left(1+2+3+......+98\right)}{1.2+2.3+3.4+.............+98.99}\) \(A=\dfrac{1+3+6+................+4851}{2+6+12+..........+9702}\)

\(A=\dfrac{1+3+6+..........+4851}{1.2+2.3+2.6+........+2.4851}\)

\(A=\dfrac{1}{2}\)

Vậy\(A=\dfrac{1}{2}\)