Question

A = \(\dfrac{7}{10x11}\) + \(\dfrac{7}{11x12}\) + \(\dfrac{7}{12x13}\) +... + \(\dfrac{7}{69x70}\)

Answer 1

`A=7/(10*11)+7/(11*12)+7/(12*13)+...+7/(69*70)`

`1/7A=1/(10*11)+1/(11*12)+1/(12*13)+..+1/(69*70)`

`1/7A=1/10-1/11+1/11-1/12+1/12-1/13+...+1/69-1/70`

`1/7A=1/10-1/70`

`1/7A=7/70-1/70`

`1/7A=6/70`

`A=3/5`

Answer 2

\(A=\dfrac{7}{10.11}+\dfrac{7}{11.12}+\dfrac{7}{12.13}+...+\dfrac{7}{69.70}\)

\(A=7.\left(\dfrac{1}{10.11}+\dfrac{1}{11.12}+\dfrac{1}{12.13}+...+\dfrac{1}{69.70}\right)\)

\(A=7\left(\dfrac{11-10}{10.11}+\dfrac{12-11}{11.12}+\dfrac{13-12}{12.13}+...+\dfrac{70-69}{69.70}\right)\)

\(A=7.\left(\dfrac{1}{10}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{13}+...+\dfrac{1}{69}-\dfrac{1}{70}\right)\)

\(A=7.\left(\dfrac{1}{10}-\dfrac{1}{70}\right)\)

\(A=7.\dfrac{3}{35}=\dfrac{3}{5}\)

Answer 3

giúp mik với

Answer 4

\(A=\dfrac{7}{10\times11}+\dfrac{7}{11\times12}+\dfrac{7}{12\times13}+...+\dfrac{7}{69\times70}\)

\(A=7\times\left(\dfrac{1}{10\times11}+\dfrac{1}{11\times12}+\dfrac{1}{12\times13}+...+\dfrac{1}{69\times70}\right)\)

\(A=7\times\left(\dfrac{1}{10}-\dfrac{1}{11}\right)+\left(\dfrac{1}{11}-\dfrac{1}{12}\right)+\left(\dfrac{1}{12}-\dfrac{1}{13}\right)+...+\left(\dfrac{1}{69}-\dfrac{1}{70}\right)\)

\(A=7\times\left(\dfrac{1}{10}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{13}+...+\dfrac{1}{69}-\dfrac{1}{70}\right)\)

\(A=7\times\left(\dfrac{1}{10}-\dfrac{1}{70}\right)\)

\(A=7\times\left(\dfrac{7}{70}-\dfrac{1}{70}\right)\)

\(A=7\times\dfrac{6}{70}\)

\(A=\dfrac{3}{5}\)

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