Question

Tính 

\(P=\sqrt{1+2015^2+\frac{2015^2}{2016^2}}+\frac{2015}{2016}\)

Answer 1

\(\sqrt{1+n^2+\frac{n^2}{\left(n+1\right)^2}}=\sqrt{\left(1+n-\frac{n}{n+1}\right)^2}=1+n-\frac{n}{n+1}\text{ }\left(n>0\right)\)

\(P==1+2015-\frac{2015}{2016}+\frac{2015}{2016}=2016\)

Answer 2

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

\(=1+n^2+\frac{n^2}{\left(n+1\right)^2}+2.\frac{n^2+n-n-n^2}{n+1}\)

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

Answer 3

Sao mr. Lazy làm nhiều thế?