Toán hsg 6!!!

C

chaugiang81

$\dfrac{1}{3}$ + $\dfrac{1}{6}$ +$\dfrac{1}{10}$ +...+ $\dfrac{2}{x^{2} -x}$= $\dfrac{49}{50}$
\Leftrightarrow $\dfrac{1}{2}$ ($\dfrac{1}{3}$ + $\dfrac{1}{6}$ +$\dfrac{1}{10}$ +...+ $\dfrac{2}{x^{2} -x}$) = ($\dfrac{49}{50}$) *$\dfrac{1}{2}$
\Rightarrow $\dfrac{1}{6}$ + $\dfrac{1}{12}$ +$\dfrac{1}{20}$ +...+ $\dfrac{1}{x^{2} -x}$ = $\dfrac{49}{100}$
\Leftrightarrow $\dfrac{1}{2*3}$ + $\dfrac{1}{3*4}$ + $\dfrac{1}{4*5}$ +...+ $\dfrac{1}{x(x-1)}$ =$\dfrac{49}{100}$
\Leftrightarrow $\dfrac{1}{2}$ - $\dfrac{1}{3}$ + $\dfrac{1}{3}$ - $\dfrac{1}{4}$ +....+ $\dfrac{1}{x-1}$ - $\dfrac{1}{x}$ = $\dfrac{49}{100}$
\Leftrightarrow $\dfrac{1}{2}$ - $\dfrac{1}{x}$ = $\dfrac{49}{100}$
tới đó tự tính x nhé :)
 
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