Đáp án:
$x$ = 305
Giải thích các bước giải:
a, $\frac{1}{5.8}$ + $\frac{1}{8.11}$ + $\frac{1}{11.14}$ + .....+ $\frac{1}{x.(x+3)}$ = $\frac{101}{1540}$
$⇔ \frac{1}{3}$ ( $\frac{1}{5}$ - $\frac{1}{8}$ + $\frac{1}{8}$ - $\frac{1}{11}$ + $\frac{1}{11}$ - $\frac{1}{14}$+......+$\frac{1}{x}$ - $\frac{1}{x+3}$) = $\frac{101}{1540}$
$⇔ \frac{1}{3}$. ( $\frac{1}{5}$ - $\frac{1}{x+3}$) = $\frac{101}{1540}$
$⇔ \frac{1}{5}$ - $\frac{1}{x+3}$ = $\frac{303}{1540}$
$⇔\frac{1}{x+3}$ = $\frac{1}{308}$
$⇔ x+3 = 308$
$⇔x = 305$
Vậy $x= 305$
