D = 1/2 + 5/6 + 11/12 + .........+ 9899/9900 Tính tổng DDDDDDD

$D$ = $\dfrac{1}{2}$ + $\dfrac{5}{6}$ + $\dfrac{11}{12}$ +..........+ $\dfrac{9899}{9900}$ 

= $($ $1$ - $\dfrac{1}{2}$ $)$ + $($ $1$ - $\dfrac{1}{6}$ $)$ +...........+ $($ $1$ - $\dfrac{1}{9900}$ $)$

= $($ $1$ + $1$ +.......+ $1$ $)$ - $($ $\dfrac{1}{1.2}$ + $\dfrac{1}{2.3}$ +.......+ $\dfrac{1}{99.100}$ $)$

Số các số $1$ là:

   $($ $99$ - $1$ $)$ : $1$ + $1$ = $99$ $($ số  $)$

$D$ = $99$ - $($ $1$ - $\dfrac{1}{100}$ $)$ = $99$ - $1$ + $\dfrac{1}{100}$ 

= $98$ + $\dfrac{1}{100}$ = $\dfrac{9081}{100}$ 

$#Ly CiiN$