Question

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Answer 1

\(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+...+\dfrac{1}{2021\times2022}\)
\(=\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+....\dfrac{1}{2021}-\dfrac{1}{2022}\)
\(=1-\dfrac{1}{2022}\)

\(=\dfrac{2021}{2022}\)

Answer 2

1/1-1/2+1/2-1/3+1/3-1/4+...+1/2021-1/2022

1-1/2022=2021/2022