Ta có
$1 + 2 + 3 = \dfrac{3 \times 4}{2}$
Suy ra
$\dfrac{1}{1 + 2 + 3} = \dfrac{2}{3 \times 4}$
Tương tự ta có
$\dfrac{1}{1 + 2 + 3 + 4} = \dfrac{2}{4 \times 5}$
...
$\dfrac{1}{1 + 2 + \cdots + 99} = \dfrac{2}{99 \times 100}$
Suy ra ptrinh trở thành
$\dfrac{2}{3\times 4} + \dfrac{2}{4\times 5} + \cdots + \dfrac{2}{99 \times 100} = \dfrac{x}{150}$
$<-> \dfrac{1}{3 \times 4} + \dfrac{1}{4 \times 5} + \cdots + \dfrac{1}{99 \times 100} = \dfrac{x}{300}$
$<-> \dfrac{1}{3} - \dfrac{1}{4} + \dfrac{1}{4} - \dfrac{1}{5} + \cdots + \dfrac{1}{99} - \dfrac{1}{100} = \dfrac{x}{300}$
$<-> \dfrac{1}{3} - \dfrac{1}{100} = \dfrac{x}{300}$
$<-> \dfrac{100 - 3}{300} = \dfrac{x}{300}$
$<-> x = 97$
Vậy $x = 97$.
