Question

Câu 7: Tính bằng cách hợp lí:
a) 2022 x 2005 - 2000 x 2022 + 15 x 2022 - 20 x 2021
b) 1/2 + 1/6 + 1/12 + 1/20 +...+ 1/342 + 1/380
Giúp mik với 🤭

Answer 1

`b) 1/2 + 1/6 + 1/12 + 1/20 +...+ 1/342 + 1/380`

`1/2 + 1/6 +1/12+....+1/380`

`=1/(1.2)+1/(2.3)+1/(3.4)+...+1/(19.20)`

`=1/1-1/2+1/2-1/3+1/3-1/4+.....+1/19-1/20`

`=1-1/20`

`=19/20`

`#Sal_tSea`

Answer 2

`a, = 2022 xx (2005 - 2000 + 15 ) - 20 xx 2021`

`= 2022 xx 20 - 20 xx 2021`

`= 20 xx (2022 - 2021)`

`= 20.`

`b, 1/2 + 1/6 + ... + 1/380`

`= 1/(1.2) + 1/(2.3) + ... + 1/(19.20)`

`= 1/1 - 1/2 + 1/2 - 1/3 + ... + 1/19 - 1/20`

`= 1/1 - 1/20`

`= 19/20`

Answer 3

\(\text{​​}\text{a},=2022\left(2005-2000+15\right)-20.2021=2022\left(20\right)-20.2021=20\left(2022-2021\right)=20.1=20\\ b,=\dfrac{1}{2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+.....+\dfrac{1}{18.19}+\dfrac{1}{19.20}\\ =\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{18}-\dfrac{1}{19}+\dfrac{1}{19}-\dfrac{1}{20}\\ =\dfrac{1}{2}-\dfrac{1}{20}\\ =\dfrac{1.10-1}{20}=\dfrac{9}{20}\)