Tinh nhanh 1 1 1 1 ____+_____+_______……..______ 1*2 2*3 3*4 9*10

0 bình luận về “Tinh nhanh 1 1 1 1 ____+_____+_______……..______ 1*2 2*3 3*4 9*10”

1. $\dfrac{1}{1×2}$ `+` $\dfrac{1}{2×3}$ `+` $\dfrac{1}{3×4}$ `+ …… +` $\dfrac{1}{9×10}$

   `=` $\dfrac{1}{1}$ `-`  $\dfrac{1}{2}$ `+` $\dfrac{1}{2}$ `-`  $\dfrac{1}{3}$ `+` $\dfrac{1}{3}$ `-`  $\dfrac{1}{4}$ `+ … +` $\dfrac{1}{9}$ `-`  $\dfrac{1}{10}$

   `=` $\dfrac{1}{1}$ `-` $\dfrac{1}{10}$

   `=` $\dfrac{9}{10}$

   Bình luận

2. `1/(1.2) + 1/(2.3) + 1/(3.4) + …. + 1/(9.10)`

   `= 1/1 – 1/2 + 1/2 – 1/3 + 1/3 – 1/4 + …. + 1/9 – 1/10`

   `= 1 – ( 1/2 – 1/2 ) – ( 1/3 – 1/3 ) – ….. – ( 1/9 – 1/9 ) – 1/10`

   `= 1 – 0 – 0 – …….. – 0 – 1/10`

   `= 1 – 1/10`

   `= 9/10`

    

   Bình luận