Question

tính giá trị biểu thức một cách hợp lí:

P=\(\frac{2}{1\times2}+\frac{2}{2\times3}+\frac{2}{3\times4}+...+\frac{2}{2013\times2014}\)

 

Answer 1

\(P=2.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.......+\frac{1}{2013}-\frac{1}{2014}\right)\)

\(P=2.\left(1-\frac{1}{2014}\right)\)

\(P=2.\frac{2013}{2014}\)

\(P=\frac{2013}{1007}\)

Answer 2

\(P=\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{2013.2014}\)

\(P=\frac{1}{2}\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2013.2014}\right)\)

\(P=\frac{1}{2}\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2013}-\frac{1}{2014}\right)\)

\(P=\frac{1}{2}\left(1-\frac{1}{2014}\right)\)

\(P=\frac{1}{2}.\frac{2013}{2014}\)

\(P=\frac{2013}{4028}\)