Question

1/5x10+1/10x15/+1/15x20+...+1/995x1000

 

Answer 1

Đặt `A = 1/(5 xx 10) + 1/(10 xx 15) + ... + 1/(995 xx 1000)`

`5A = 5 xx ( 1/(5 xx 10) + 1/(10 xx 15) + ... + 1/(995 xx 1000))`

`5A =  5/(5 xx 10) + 5/(10 xx 15) + ... + 5/(995 xx 1000)`

`5A = 1/5 - 1/10 + 1/10 - 1/15 + .... + 1/995 - 1/1000`

`5A = 1/5 - 1/1000`

`5A = 199/1000`

`A = 199/5000`

Answer 2

\(\dfrac{1}{5.10}+\dfrac{1}{10.15}+...+\dfrac{1}{995.1000} \\ =\dfrac{1}{5}\left(\dfrac{1}{5}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{15}+...+\dfrac{1}{995}-\dfrac{1}{1000}\right)\\ =\dfrac{1}{5}\left(\dfrac{1}{5}-\dfrac{1}{1000}\right)\\ =\dfrac{1}{5}.\dfrac{199}{1000}=\dfrac{199}{5000}\)