Đáp án:
$\text{ $\dfrac{99}{20}$}$
Giải thích các bước giải:
$\text{Đặt A = $\dfrac{5}{2}$ + $\dfrac{5}{6}$ + $\dfrac{5}{12}$ +...+ $\dfrac{5}{9900}$}$
$\text{= 5($\dfrac{1}{2}$ + $\dfrac{1}{6}$ + $\dfrac{1}{12}$ +...+ $\dfrac{1}{9900}$)}$
$\text{= 5($\dfrac{1}{1.2}$ + $\dfrac{1}{2.3}$ + $\dfrac{1}{3.4}$ +...+ $\dfrac{1}{99.100}$)}$
$\text{= 5(1 - $\dfrac{1}{2}$ + $\dfrac{1}{2}$ - $\dfrac{1}{3}$ + $\dfrac{1}{3}$ - $\dfrac{1}{4}$ +...+ $\dfrac{1}{99}$ - $\dfrac{1}{100}$}$
$\text{= 5 - $\dfrac{1}{20}$}$
$\text{= $\dfrac{100}{20}$ - $\dfrac{1}{20}$}$
$\text{= $\dfrac{99}{20}$}$
$\text{Vậy A = $\dfrac{99}{20}$}$
$#Zero#$
$#Hoidap247#$
