Giải thích các bước giải:
Ta có :
$\dfrac{a}{x(x+a)}+\dfrac{a}{(x+a)(x+2a)}+\dfrac{a}{(x+2a)(x+3a)}+..+\dfrac{a}{(x+9a)(x+10a)}+\dfrac{1}{x+10a}$
$=\dfrac{x+a-x}{x(x+a)}+\dfrac{x+2a-(x+a)}{(x+a)(x+2a)}+\dfrac{(x+3a)-(x+2a)}{(x+2a)(x+3a)}+..+\dfrac{x+10a-(x+9a)}{(x+9a)(x+10a)}+\dfrac{1}{x+10a}$
$=\dfrac{1}{x}-\dfrac{1}{x+a}+\dfrac{1}{x+a}-\dfrac{1}{x+2a}+..+\dfrac{1}{x+9a}-\dfrac{1}{x+10a}+\dfrac{1}{x+10a}$
$=\dfrac{1}{x}$
