Question

[Phan Thị Xoan]

Tính:

B= 7/45+7/117+7/221+7/357+7/525

Answer 1

[Nguyễn Tuấn Tú]

\(B=\dfrac{7}{45}+\dfrac{7}{117}+\dfrac{7}{221}+\dfrac{7}{357}+\dfrac{7}{525}\)

\(B=\dfrac{7}{5\times9}+\dfrac{7}{9\times13}+\dfrac{7}{13\times17}+\dfrac{7}{17\times21}+\dfrac{7}{21\times25}\)

\(B=\dfrac{7}{4}\times\left(\dfrac{1}{5}-\dfrac{1}{9}\right)+\dfrac{7}{4}\times\left(\dfrac{1}{9}-\dfrac{1}{13}\right)+\dfrac{7}{4}\times\left(\dfrac{1}{13}-\dfrac{1}{17}\right)+\dfrac{7}{4}\times\left(\dfrac{1}{17}-\dfrac{1}{21}\right)+\dfrac{7}{4}\times\left(\dfrac{1}{21}-\dfrac{1}{25}\right)\)

\(B=\dfrac{7}{4}\times\left(\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{17}+\dfrac{1}{17}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{25}\right)\)

\(B=\dfrac{7}{4}\times\left(\dfrac{1}{5}-\dfrac{1}{25}\right)\)

\(B=\dfrac{7}{4}\times\dfrac{4}{25}\)

\(B=\dfrac{7}{25}\)

Vậy \(B=\dfrac{7}{25}\)