Question

a, so sánh: \(\sqrt{17}+\sqrt{26}+1\)và \(\sqrt{99}\)

b, CMR: \(\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+...+\frac{1}{\sqrt{100}}\)>10

Answer 1

a) \(\sqrt{17}>\sqrt{16}=4\); \(\sqrt{26}>\sqrt{25}=5\) => \(\sqrt{17}+\sqrt{26}+1>4+5+1=10=\sqrt{100}>\sqrt{99}\)

Vậy \(\sqrt{17}+\sqrt{26}+1>\sqrt{99}\)

b) \(\frac{1}{\sqrt{1}}>\frac{1}{\sqrt{100}};\frac{1}{\sqrt{2}}>\frac{1}{\sqrt{100}};...;\frac{1}{\sqrt{99}}>\frac{1}{\sqrt{100}}\)

=> \(\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+...+\frac{1}{\sqrt{100}}>\frac{1}{\sqrt{100}}+\frac{1}{\sqrt{100}}+...+\frac{1}{\sqrt{100}}=\frac{100}{\sqrt{100}}=10\)

Vậy.....