A= $\dfrac{-1}{20}$ + $\dfrac{-1}{30}$ + $\dfrac{-1}{42}$ $\dfrac{-1}{56}$ + $\dfrac{-1}{72}$ $\dfrac{-1}{90}$ tính tổng AAAAAAAaaaaaaa

Đáp án:

$\text{A = `-3/20`}$

Giải thích các bước giải:

$\text{A = -($\dfrac{1}{4.5}$ + $\dfrac{1}{5.6}$ + .... + $\dfrac{1}{9.10}$)}$

$\text{A = -($\dfrac{1}{4}$ - $\dfrac{1}{5}$ + $\dfrac{1}{5 - ...... - $\dfrac{1}{10}$)}$

$\text{A = -($\dfrac{1}{4}$ - $\dfrac{1}{10}$)}$

$\text{A = `-3/20`}$

`A = -1/20 + {-1}/30 + {-1}/42 + {-1}/56 + {-1}/72 + {-1}/90`

`A = -1/20 - 1/30 - 1/42 - 1/56 - 1/72 - 1/90`

`A = -( 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90 )`

`A = -( 1/{4.5} + 1/{5.6} + 1/{6.7} + 1/{7.8} + 1/{8.9} + 1/{9.10} )`

`A = -( 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + 1/7  - 1/8 + 1/8 - 1/9 + 1/9 - 1/10 )`

`A = -( 1/4 - 1/10 ) `

`A = -3/20`

$Vậy$ `A = -3/20`