Question

Rút gọn biểu thức sau:

\(\frac{2014}{\sqrt{1}+\sqrt{2}}+\frac{2014}{\sqrt{2}+\sqrt{3}}+...+\frac{2014}{\sqrt{99}+\sqrt{100}}\)

Answer 1

\(\frac{2014}{\sqrt{1}+\sqrt{2}}+\frac{2014}{\sqrt{2}+\sqrt{3}}+...+\frac{2014}{\sqrt{99}+\sqrt{100}}\)

\(=2014.\left(\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+...+\frac{1}{\sqrt{99}+\sqrt{100}}\right)\)

\(=2014.\left(\sqrt{2}-\sqrt{1}+\sqrt{3}-\sqrt{2}+...+\sqrt{100}-\sqrt{99}\right)\)

\(=2014.\left(\sqrt{100}-\sqrt{1}\right)=2014.9=18126\)

Answer 2

\(\frac{2014}{\sqrt{1}+\sqrt{2}}+\frac{2014}{\sqrt{2}+\sqrt{3}}+.....+\frac{2014}{\sqrt{9}+\sqrt{100}}\)

\(=\sqrt{1}-\sqrt{2}+\sqrt{3}-\sqrt{2}+....+\sqrt{100}-\sqrt{999}\)

\(=\sqrt{100}-1\)

\(=9\)

P/s: Không chắc à

Answer 3

\(\frac{2014}{\sqrt{1}+\sqrt{2}}+\frac{2014}{\sqrt{2}+\sqrt{3}}+....+\frac{2014}{\sqrt{99}+\sqrt{100}}\)

\(=\sqrt{1}-\sqrt{2}+\sqrt{3}-\sqrt{2}+....+\sqrt{100}-\sqrt{99}\)

\(=\sqrt{100}-1\)

\(=9\)

\(=9.2014=18126\)