Câu hỏi 15
Chứng minh rằng: $$
\frac{2}{x^{2} - 1} + \frac{4}{x^{2} - 4} + \frac{6}{x^{2} - 9} + \ldots + \frac{20}{x^{2} - 100} =
$$ $$
\frac{11}{(x - 1)(x + 10)} + \frac{11}{(x - 2)(x + 9)} + \ldots + \frac{11}{(x - 10)(x + 1)}.
$$
\frac{2}{x^{2} - 1} + \frac{4}{x^{2} - 4} + \frac{6}{x^{2} - 9} + \ldots + \frac{20}{x^{2} - 100} =
$$ $$
\frac{11}{(x - 1)(x + 10)} + \frac{11}{(x - 2)(x + 9)} + \ldots + \frac{11}{(x - 10)(x + 1)}.
$$