Question

tính

\(\frac{10}{1+\sqrt{4}}+\frac{10}{\sqrt{4}+\sqrt{7}}+\frac{10}{\sqrt{7}+\sqrt{10}}+...+\frac{10}{\sqrt{97}+\sqrt{100}}\)

Answer 1

=\(\frac{10\left(\sqrt{4}-1\right)}{4-1}+\frac{10\left(\sqrt{7}-1\right)}{7-4}+\frac{10\left(\sqrt{10}-\sqrt{7}\right)}{10-7}+...+\frac{10\left(\sqrt{100}-\sqrt{97}\right)}{100-97}\)

=\(\frac{10}{3}+\frac{10\sqrt{7}-10}{3}+\frac{10\sqrt{10}-10\sqrt{7}}{3}+...+\frac{10\sqrt{100}-10\sqrt{97}}{3}\)

=\(\frac{1}{3}\left(10+10\sqrt{7}-10+10\sqrt{10}-10\sqrt{7}+...+10\sqrt{100}-10\sqrt{97}\right)\)

=\(\frac{1}{3}\left(10\sqrt{100}-10\right)\)

=30