Đáp án: x = $\frac{97}{4950}$
Giải thích các bước giải:
x - $\frac{1}{2}$ + x - $\frac{1}{6}$ + x - $\frac{1}{12}$ + x - $\frac{1}{20}$ + ..... + x - $\frac{1}{9900}$ = $\frac{19}{20}$
( x + x + x + x + ..... + x ) - ( $\frac{1}{2}$ + $\frac{1}{6}$ + $\frac{1}{12}$ + $\frac{1}{20}$ + ..... + $\frac{1}{9900}$ ) = $\frac{19}{20}$
( x + x + x + x + ..... + x ) - ( $\frac{1}{1.2}$ + $\frac{1}{2.3}$ + $\frac{1}{3.4}$ + $\frac{1}{4.5}$ + ..... + $\frac{1}{99.100}$ ) = $\frac{19}{20}$
x . 99 - ( 1 - $\frac{1}{2}$ + $\frac{1}{2}$ - $\frac{1}{3}$ + $\frac{1}{3}$ - $\frac{1}{4}$ + $\frac{1}{4}$ - $\frac{1}{5}$ + ..... + $\frac{1}{99}$ - $\frac{1}{100}$ ) = $\frac{19}{20}$
x . 99 - ( 1 - $\frac{1}{100}$ ) = $\frac{19}{20}$
x . 99 - $\frac{99}{100}$ = $\frac{19}{20}$
x . 99 = $\frac{19}{20}$ + $\frac{99}{100}$
x . 99 = $\frac{97}{50}$
x = $\frac{97}{50}$ : 99
x = $\frac{97}{4950}$
