Question

M= \(\dfrac{1}{\sqrt{2}-\sqrt{3}}-\dfrac{1}{\sqrt{3}-\sqrt{4}}+\dfrac{1}{\sqrt{4}-\sqrt{5}}-....+\dfrac{1}{\sqrt{100}-\sqrt{101}}\)

Answer 1

ta có : \(M=\dfrac{1}{\sqrt{2}-\sqrt{3}}-\dfrac{1}{\sqrt{3}-\sqrt{4}}+\dfrac{1}{\sqrt{4}-\sqrt{5}}-...+\dfrac{1}{\sqrt{100}-\sqrt{101}}\)

\(=\dfrac{\sqrt{2}+\sqrt{3}}{-1}-\dfrac{\sqrt{3}+\sqrt{4}}{-1}+\dfrac{\sqrt{4}+\sqrt{5}}{-1}-...+\dfrac{\sqrt{100}+\sqrt{101}}{-1}\)

\(=-\sqrt{2}-\sqrt{3}+\sqrt{3}+\sqrt{4}-\sqrt{4}-\sqrt{5}+...-\sqrt{100}-\sqrt{101}\)

\(=-\sqrt{2}-\sqrt{100}-\sqrt{101}\) (xem kỉ chút là hiểu thôi)

Answer 2

Mysterious Person giúp mk nha