Câu hỏi của Virgo Cá Tính

Question

B = (1+1/1.3)(1+1/2.4)(1+1/3.5)......(1+1/2014.2016)(1+ 1/2015.2017) Nếu có thể thì các bạn giải ra giùm mik nha

Bui Thi Minh Thu · Accepted Answer

Chào bạn !Mình kết bạn nha!Câu trả lời: Chào bạn !Mình kết bạn nha!

Hoàng Minh Hoài · Answer

$B=\frac{3+1}{3}+\frac{8+1}{8}+...+\frac{2014.2016+1}{2014.2016}+\frac{2015.2017+1}{2015.2017}$         $=\frac{2^2}{3}+\frac{3^2}{8}+....+\frac{2015^2}{2014.2016}+\frac{2016^2}{2015.2017}$         =$\frac{2.2}{3}+\frac{3.3}{2.4}+...+\frac{2015.2015}{2014.2016}+\frac{2016.2016}{2015.2017}$         =$\frac{\left(2.3....2015.2016\right)+\left(2.3.....2015.2016\right)}{\left(1.2.3.....2014.2015\right)+\left(3.4....2016.2017\right)}$         =$2016+\frac{2}{2017}$                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  Câu trả lời:                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  $B=\frac{3+1}{3}+\frac{8+1}{8}+...+\frac{2014.2016+1}{2014.2016}+\frac{2015.2017+1}{2015.2017}$         $=\frac{2^2}{3}+\frac{3^2}{8}+....+\frac{2015^2}{2014.2016}+\frac{2016^2}{2015.2017}$         =$\frac{2.2}{3}+\frac{3.3}{2.4}+...+\frac{2015.2015}{2014.2016}+\frac{2016.2016}{2015.2017}$         =$\frac{\left(2.3....2015.2016\right)+\left(2.3.....2015.2016\right)}{\left(1.2.3.....2014.2015\right)+\left(3.4....2016.2017\right)}$         =$2016+\frac{2}{2017}$

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