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

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

mỗi câu làm 1 yếu tố đc k bn?

a)\(\frac{18}{-39}=-\frac{18}{39}\)

Vì -17>-18 nên \(-\frac{17}{39}>-\frac{18}{39}\)(1)

Vì 39<41 nên \(-\frac{17}{39}< -\frac{17}{41}\)(2)

Từ (1);(2)=>\(\frac{-18}{39}< -\frac{17}{39}< -\frac{17}{41}\)

b)Ta có: \(\frac{42}{-37}=-\frac{42}{37}>\frac{-42}{35}=\frac{-6}{5}=-1,2\); \(-\frac{56}{43}< -\frac{55}{43}< -\frac{55}{44}=-\frac{5}{4}=-1,25\)

Vì -1,2>-1,25 nên 42/-37>-56/43

c)Ta có:25049<25259 hay 37*677<67*377 nên 37/67<377/677

d)Ta có:\(\frac{5}{8}=\frac{10}{16}< \frac{34}{16}=\frac{17}{8}< \frac{17}{19}\); \(\frac{17}{19}< 1;\frac{22}{17}>1=>\frac{22}{17}>\frac{17}{19}\)

=>\(\frac{22}{17}>\frac{17}{19}>\frac{5}{8}\)

làm hơi lâu

dc bn, giúp mk zới nha

Xét A-B=5-\(\sqrt{10}\)(2/3+1)= 5-\(\frac{5\sqrt{10}}{3}\)=5(1-\(\frac{\sqrt{10}}{3}\)) < 0

Vậy A<B

\(2\sqrt{10}=\sqrt{4\cdot10}=\sqrt{40}>\sqrt{36}=6\Rightarrow2\sqrt{10}>6\)

\(\Rightarrow15-2\sqrt{10}< 15-6=9\Rightarrow\frac{15-2\sqrt{10}}{3}< \frac{9}{3}=3\)mà \(3=\sqrt{9}< \sqrt{10}\Rightarrow\frac{15-2\sqrt{10}}{3}< \sqrt{10}\)

a)Ta có:\(\sqrt{17}>\sqrt{16}\)

             \(\sqrt{26}>\sqrt{25}\)

\(\implies\) \(\sqrt{17}+\sqrt{26}>\sqrt{16}+\sqrt{25}\)

\(\implies\) \(\sqrt{17}+\sqrt{26}+1>\sqrt{16}+\sqrt{25}+1=4+5+1=10\)

Mà \(\sqrt{100}=10\) \(\implies\) \(\sqrt{17}+\sqrt{26}+1>\sqrt{100}\)

Mà \(\sqrt{100}>\sqrt{99}\) \(\implies\) \(\sqrt{17}+\sqrt{26}+1>\sqrt{99}\)

b)Ta có:\(\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+....+\frac{1}{\sqrt{100}}>\frac{1}{\sqrt{100}}+\frac{1}{\sqrt{100}}+...+\frac{1}{\sqrt{100}}=100.\frac{1}{\sqrt{100}}\)

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

\(\implies\) \(\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+....+\frac{1}{\sqrt{100}}>10\left(đpcm\right)\)

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

b) \(\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+.....+\frac{1}{\sqrt{100}}>\frac{1}{\sqrt{100}}+\frac{1}{\sqrt{100}}+\frac{1}{\sqrt{100}}+.......+\frac{1}{\sqrt{100}}=\frac{100}{\sqrt{100}}=10\)

d.

\(-\frac{31}{30}< -1\)

\(-1< -\frac{45}{47}\)

\(\Rightarrow-\frac{31}{30}< -\frac{45}{47}\)

Chúc bạn học tốt

trong 4 yếu tố trên mà bn

vs lại giúp mk mấy câu kia lun

Thật sự mik ko hỉu đề bài mấy, bn ns rõ hơn đc ko?