2/5.8 + 2/8.11 + 2/11.14 + ................ + 2/x(x+3) = 101/770

Đáp án+Giải thích các bước giải:

$\dfrac{2}{5.8}$ + $\dfrac{2}{8.11}$ + $\dfrac{2}{11.14}$ +......+ $\dfrac{2}{x.(x+3)}$ = $\dfrac{101}{770}$ 

= $\dfrac{2}{3}$ . $($ $\dfrac{3}{5.8}$ + $\dfrac{3}{8.11}$ + $\dfrac{3}{11.14}$ +.......+ $\dfrac{3}{x(x+3)}$ $)$ = $\dfrac{101}{770}$ 

= $\dfrac{2}{3}$ . $($ $\dfrac{1}{5}$ - $\dfrac{1}{8}$ + $\dfrac{1}{8}$ - $\dfrac{1}{11}$ + $\dfrac{1}{11}$ - $\dfrac{1}{14}$ +......+ $\dfrac{1}{x}$ - $\dfrac{1}{x+3}$ $)$ = $\dfrac{101}{770}$ 

= $\dfrac{2}{3}$ . $($ $\dfrac{1}{5}$ + $\dfrac{1}{x+3}$ $)$ = $\dfrac{101}{770}$ 

= $\dfrac{1}{5}$ - $\dfrac{1}{x+3}$  = $\dfrac{101}{770}$ : $\dfrac{2}{3}$ = $\dfrac{303}{1540}$ 

= $\dfrac{1}{x+3}$ = $\dfrac{1}{308}$ 

= $x$ + $3$ = $308$

= $x$           =  $308$ - $3$ = $305$

Vậy $x$ = $305$