Em tham khảo nhé:
$\text{Xét 200-(3+$\dfrac{2}{3}$+$\dfrac{2}{4}$+....+$\dfrac{2}{100}$)}$
$\text{=200-2-(1+$\dfrac{2}{3}$+...+$\dfrac{2}{100}$)}$
$\text{=198-(1+$\dfrac{2}{3}$+...+$\dfrac{2}{100}$)}$
$\text{=2[99-($\dfrac{1}{2}$- $\dfrac{1}{3}$+....+ $\dfrac{1}{100}$ ) (1)}$
$\text{Xét $\dfrac{1}{2}$+$\dfrac{2}{3}$+..+ $\dfrac{99}{100}$}$
$\text{⇒Rút 1 ra (Có 99 số)}$
$\text{⇒99-( $\dfrac{1}{2}$+ $\dfrac{1}{3}$+..+$\dfrac{1}{100}$) (2)}$
$\text{Từ 1,2⇒A=2}$
