Question

Tính :

C = \(\left(1+\dfrac{1}{2.3}\right)\) \(\left(1+\dfrac{1}{2.4}\right)\) \(\left(1+\dfrac{1}{3.5}\right)\) .....\(\left(1+\dfrac{1}{2014.2016}\right)\)

Answer 1

Chắc ngoặc đầu tiên là \(\left(1+\dfrac{1}{1.3}\right)\) đúng ko bạn (mặc dù đề như bạn thì vẫn tính được)

\(1+\dfrac{1}{n\left(n+2\right)}=\dfrac{n\left(n+2\right)+1}{n\left(n+2\right)}=\dfrac{n^2+2n+1}{n\left(n+2\right)}=\dfrac{\left(n+1\right)^2}{n\left(n+2\right)}\)

\(\Rightarrow C=\dfrac{2^2.3^2...2015^2}{1.3.2.4...2014.2016}=\dfrac{2.3...2015}{1.2...2014}.\dfrac{2.3...2015}{3.4...2016}=\dfrac{2015}{1}.\dfrac{2}{2016}=\dfrac{2015}{1008}\)