Question

1/2+1/2.3+1/3.4+...+1/2021.2022

Answer 1

`1/2+1/(2.3)+1/(3.4)+...... +1/(2021.2022)`

`=1/(1.2) +1/(2.3)+1/(3.4)+...... +1/(2021.2022)`

`=1-1/2+1/2-1/3+.......+1/2021-1/2022`

`=1-1/2022`

`=2022/2022-1/2022`

`=2021/2022`

Answer 2

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{2021}-\dfrac{1}{2022}\)

=1-1/2022

=2021/2022