Question

S=1/2.3+1/3.4+1/4.5+...+1/2021+2022

 

HELP ME!!!

Answer 1

\(S=\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{2021.2022}\\ S=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{2021}-\dfrac{1}{2022}\\ S=\dfrac{1}{2}-\dfrac{1}{2022}\\ S=\dfrac{1010}{2022}=\dfrac{505}{1011}\)

`@An`

Answer 2

\(\dfrac{1}{2.3}\)+\(\dfrac{1}{3.4}\)+\(\dfrac{1}{4.5}\)+...+\(\dfrac{1}{2021.2022}\)

= \(\dfrac{1}{2}\)-\(\dfrac{1}{3}\)+\(\dfrac{1}{3}\)-\(\dfrac{1}{4}\)+...+\(\dfrac{1}{2021}\)-\(\dfrac{1}{2022}\)

= \(\dfrac{1}{2}\)-\(\dfrac{1}{2022}\)

= \(\dfrac{1011}{2022}\)-\(\dfrac{1}{2022}\)

= \(\dfrac{1010}{2022}\)= \(\dfrac{505}{1011}\)

Answer 3

\(S=\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+...+\dfrac{1}{2021+2022}\)

\(S=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{2021}+\dfrac{1}{2021}-\dfrac{1}{2022}\)

\(S=\dfrac{1}{2}-\dfrac{1}{2022}\)

\(S=\dfrac{1011}{2022}-\dfrac{1}{2022}\)

\(S=\dfrac{505}{1011}\)