\(A=\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{2021.2022}\\ =\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{2021}-\dfrac{1}{2022}\\ =\dfrac{1}{3}-\dfrac{1}{2022}\\ =\dfrac{673}{2022}\)
`A = 1/(3.4)+1/(4.5)+....+1/(2021.2022)`
`= 1/3 - 1/4 + 1/4 - 1/5 +....+1/2021-1/2022`
`= 1/3 - 1/2022`
`= 2019/6066`
`= 673/2022`
\(A=\dfrac{1}{3.4}+\dfrac{1}{4,5}+\dfrac{1}{5.6}+...+\dfrac{1}{2021.2022}\)
\(A=\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{2021}-\dfrac{1}{2022}\)
\(A=\dfrac{1}{3}-\dfrac{1}{2022}\)
\(A=\dfrac{673}{2022}\)
