Rút gọn các biểu thức,
a> A= \(\frac{1}{\sqrt{1}+\sqrt{2}}\) + \(\frac{1}{\sqrt{2}+\sqrt{3}}\)+ \(\frac{1}{\sqrt{3}+\sqrt{4}}\)+ ......... + \(\frac{1}{\sqrt{n-1}+\sqrt{n}}\)
b> B= \(\frac{1}{\sqrt{1}-\sqrt{2}}\)- \(\frac{1}{\sqrt{2}-\sqrt{3}}\)- \(\frac{1}{\sqrt{3}-\sqrt{4}}\)- .......... - \(\frac{1}{\sqrt{24}-\sqrt{25}}\)
\(A=\frac{\sqrt{2}-\sqrt{1}}{\left(\sqrt{2}-\sqrt{1}\right)\left(\sqrt{2}+\sqrt{1}\right)}+.......+\frac{\sqrt{n}-\sqrt{n-1}}{\left(\sqrt{n}-\sqrt{n-1}\right)\left(\sqrt{n}+\sqrt{n}-1\right)}\)
\(=\frac{\sqrt{2}-\sqrt{1}}{2-1}+........+\frac{\sqrt{n}-\sqrt{n-1}}{n-\left(n-1\right)}\)
\(=\sqrt{2}-\sqrt{1}+...........+\sqrt{n}-\sqrt{n-1}\)
\(=\sqrt{n}-\sqrt{1}=\sqrt{n}-1\)
bài B tương tự
