Đáp án+giải thích các bước giải:
$\dfrac{1}{1.2}$ + $\dfrac{1}{2.3}$ + $\dfrac{1}{3.4}$ +...+ $\dfrac{1}{99.100}$
= $\dfrac{1}{1}$ - $\dfrac{1}{2}$ + $\dfrac{1}{2}$ - $\dfrac{1}{3}$ + $\dfrac{1}{3}$ - $\dfrac{1}{4}$ + ...+ $\dfrac{1}{99}$ + $\dfrac{1}{100}$
= $1$ - $\dfrac{1}{100}$
= $\dfrac{99}{100}$