Question

Tính:

A=\(\dfrac{1}{1+\sqrt{2}}\)+\(\dfrac{1}{\sqrt{2}+\sqrt{3}}\)+\(\dfrac{1}{\sqrt{3}+\sqrt{4}}\)+.....+\(\dfrac{1}{\sqrt{99}+\sqrt{100}}\)

Answer 1

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

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

=10-1

=9