Question

Tính B=\(B=\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+..+\frac{1}{\sqrt{2014}+\sqrt{2015}}\)

Answer 1

nhân liên hợp  để trục căn thức ở mẫu

Answer 2

B = \(\frac{\sqrt{2}-\sqrt{1}}{\left(\sqrt{2}-\sqrt{1}\right)\left(\sqrt{2}+\sqrt{1}\right)}+\frac{\sqrt{3}-\sqrt{2}}{\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)}+...+\frac{\sqrt{2015}-\sqrt{2014}}{\left(\sqrt{2015}-\sqrt{2014}\left(\sqrt{2014}+\sqrt{2015}\right)\right)}\)

B = \(\sqrt{2}-1+\sqrt{3}-\sqrt{2}+....\sqrt{2015}-\sqrt{2014}\)  ( Tất cả mẫu đều bằng 1)

B = -1 + căn 2015 

Answer 3

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

\(B=-\sqrt{1}+\sqrt{2}-\sqrt{2}+\sqrt{3}-...-\sqrt{2014}+\sqrt{2015}=-1+\sqrt{2015}\)