Question

[BÍCH THẢO]

Help !

Tính hợp lí :

A= 1/1.6 - 1/6.11 - 1/11.16 -1/16. 21 -...- 1/46.51

Answer 1

[Toru]

\(A=\dfrac{1}{1\cdot6}-\dfrac{1}{6\cdot11}-\dfrac{1}{11\cdot16}-\dfrac{1}{16\cdot21}-...-\dfrac{1}{46\cdot51}\)

\(=\dfrac{1}{6}-\left(\dfrac{1}{6\cdot11}+\dfrac{1}{11\cdot16}+\dfrac{1}{16\cdot21}+...+\dfrac{1}{46\cdot51}\right)\)

\(=\dfrac{1}{6}-\dfrac{1}{5}\left(\dfrac{5}{6\cdot11}+\dfrac{5}{11\cdot16}+\dfrac{5}{16\cdot21}+...+\dfrac{5}{46\cdot51}\right)\)

\(=\dfrac{1}{6}-\dfrac{1}{5}\left(\dfrac{1}{6}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+...+\dfrac{1}{46}-\dfrac{1}{51}\right)\)

\(=\dfrac{1}{6}-\dfrac{1}{5}\left(\dfrac{1}{6}-\dfrac{1}{51}\right)\)

\(=\dfrac{1}{6}-\dfrac{1}{5}\cdot\dfrac{5}{34}\)

\(=\dfrac{1}{6}-\dfrac{1}{34}\)

\(=\dfrac{7}{51}\)

Vậy \(A=\dfrac{7}{51}\)

Answer 2

[BÍCH THẢO]

C.ơn chị ah.