Question

tính giá trị iểu thức  = \(\left(1+\frac{1}{13}\right).\left(1+\frac{1}{24}\right).\left(1+\frac{1}{35}\right).....\left(1+\frac{1}{2014}\right).2016\)

Answer 1

mk sữa lại \(\left(1+\frac{1}{1.3}\right).\left(1+\frac{1}{24}\right).\left(1+\frac{1}{35}\right).....\left(1+\frac{1}{2014.2016}\right)\)

Answer 2

mk sửa lạ là 1.3 

2.4

3.5

Answer 3

Đặt A=\(\left(1+\frac{1}{1.3}\right).\left(1+\frac{1}{2.4}\right).\left(1+\frac{1}{3.5}\right)........\left(1+\frac{1}{2014.2016}\right)\)

      A=\(\frac{1.3+1}{1.3}.\frac{2.4+1}{2.4}.\frac{3.5+1}{3.5}..............\frac{2014.2016+1}{2014.2016}\)

     A=\(\frac{4}{1.3}.\frac{9}{2.4}.\frac{16}{3.5}..............\frac{4060225}{2014.2016}\)

   A=\(\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}...............\frac{2015^2}{2014.2016}\)

  A=\(\frac{\left(2.3.4.............2015\right).\left(2.3.4............2015\right)}{\left(1.2.3............2014\right).\left(3.4.5.....................2016\right)}\)

  A=\(\frac{2015.2}{1.2016}\)

A=\(\frac{2015.2}{1008.2}=\frac{2015}{1008}\)

Vậy A=\(\frac{2015}{1008}\)

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