Question

thực hiện phép tính B=10/7.12+10/12.17+10/17.22+...+10/2017.2022 GIÚP MÌNH VỚI NHA

Answer 1

\(B=\frac{10}{7.12}+\frac{10}{12.17}+\frac{10}{17.22}+...+\frac{10}{2017.2022}\)

\(=2\left(\frac{5}{7.12}+\frac{5}{12.17}+\frac{5}{17.22}+...+\frac{5}{2017.2022}\right)\)

\(=2\left(\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{17}+...+\frac{1}{2017}-\frac{1}{2022}\right)\)

\(=2\left(\frac{1}{7}-\frac{1}{2022}\right)=\frac{2015}{7077}\)

Answer 2

\(B=\frac{10}{7.12}+\frac{10}{12.17}+\frac{10}{17.22}+...+\frac{10}{2017.2022}\)

\(\Rightarrow B=2.\left(\frac{5}{7.12}+\frac{5}{12.17}+\frac{5}{17.22}+...+\frac{5}{2017.2022}\right)\)

\(\Rightarrow B=2.\left(\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{17}+\frac{1}{17}-\frac{1}{22}+...+\frac{1}{2017}-\frac{1}{2022}\right)\)

\(\Rightarrow B=2.\left(\frac{1}{7}-\frac{1}{2022}\right)\)

\(\Rightarrow B=2.\frac{2015}{14154}\)

\(\Rightarrow B=\frac{2015}{7077}.\)

Vậy \(B=\frac{2015}{7077}.\)

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