Question

Rút gọn:

\(\frac{1}{\sqrt{1}\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+...+\frac{1}{\sqrt{24}\sqrt{25}}\)

Answer 1

\(\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+...+\frac{1}{\sqrt{24}+\sqrt{25}}\)

\(=\frac{\left(\sqrt{2}-\sqrt{1}\right)\left(\sqrt{2}+\sqrt{1}\right)}{\sqrt{1}+\sqrt{2}}+\frac{\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)}{\sqrt{2}+\sqrt{3}}\)

\(+...+\frac{\left(\sqrt{25}-\sqrt{24}\right)\left(\sqrt{25}+\sqrt{24}\right)}{\sqrt{24}+\sqrt{25}}\)

\(=\sqrt{2}-\sqrt{1}+\sqrt{3}-\sqrt{2}+...+\sqrt{25}-\sqrt{24}\)

\(=\sqrt{25}-1=5-1=4\)

Answer 2

\(\frac{1}{\sqrt{1}\sqrt{2}}+\frac{1}{\sqrt{2}\sqrt{3}}+...+\frac{1}{\sqrt{24}\sqrt{25}}\)

\(=\frac{1}{\sqrt{1}}-\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{24}}-\frac{1}{\sqrt{25}}\)

\(=\frac{1}{\sqrt{1}}-\frac{1}{\sqrt{25}}\)

Answer 3

Khó quá

Answer 4

lớp 7 chưa học căn thức mà Sát Long Nhân Natsu

Answer 5

hok oy mak

Answer 6

I don't no ~~~

Answer 7

Chịu thoi ~

Answer 8

Sai đề bài rùi

Answer 9

mk lp , 2k7 nên...