Ta có :

\(\frac{1}{51}\)> \(\frac{1}{100}\)

\(\frac{1}{52}\)> \(\frac{1}{100}\)

      ...

\(\frac{1}{99}\)> \(\frac{1}{100}\)

\(\frac{1}{100}\)= \(\frac{1}{100}\)

=> S > 50 x \(\frac{1}{100}\)

=> S > \(\frac{50}{100}\)= \(\frac{1}{2}\)

Vậy S > \(\frac{1}{2}\)

\(S=\frac{1}{51}+\frac{1}{52}+\frac{1}{53}+...+\frac{1}{100}\)

Ta có \(\frac{1}{51}>\frac{1}{100}\)

        \(\frac{1}{52}>\frac{1}{100}\)

               ...

        \(\frac{1}{99}>\frac{1}{100}\)

\(\Rightarrow\frac{1}{51}+\frac{1}{52}+\frac{1}{53}+...+\frac{1}{99}+\frac{1}{100}>\frac{1}{100}+\frac{1}{100}+\frac{1}{100}+...+\frac{1}{100}\)

                                                                                         ( có 50 phân số)

\(\Rightarrow S>50.\frac{1}{100}\)

\(\Rightarrow S>\frac{1}{2}\)

Vậy...

Bài làm

Ta thấy: \(\frac{1}{51}+\frac{1}{52}+\frac{1}{53}+...+\frac{1}{99}+\frac{1}{100}\)có 50 số hạng

=> \(\frac{1}{51}+\frac{1}{52}+\frac{1}{53}+...+\frac{1}{99}\)có 49 số hạng

Và \(\frac{1}{51}+\frac{1}{52}+\frac{1}{53}+...+\frac{1}{99}\)luôn lớn hơn \(\frac{1}{100}\)

Ta có: \(\frac{1}{100}\Rightarrow\frac{1}{100}.50=\frac{50}{100}=\frac{1}{2}\)

=> \(\frac{1}{100}=\frac{1}{2}\)

=> \(\frac{1}{51}+\frac{1}{52}+\frac{1}{53}+...+\frac{1}{99}>\frac{1}{2}\)

\(\Rightarrow\frac{1}{51}+\frac{1}{52}+\frac{1}{53}+...+\frac{1}{99}+\frac{1}{100}>\frac{1}{2}\)

Vậy S > 1/2

# Học tốt #

a)327/215>619/215

b)-33/131<53/-217

c)22/-67>-51/152

Ngô Thanh Hải bn giải ra cụ thể giúp mik đc k

a) \(\frac{327}{215}\)> \(\frac{691}{428}\)

b) \(\frac{-33}{131}\)<\(\frac{53}{-217}\)

c)\(\frac{22}{-67}\)>\(\frac{-51}{152}\)

a) \(\frac{67}{77}=1-\frac{10}{77};\frac{73}{83}=1-\frac{10}{83}\)

Vì \(\frac{10}{77}>\frac{10}{83}\) nên \(1-\frac{10}{77}

h tui k tui giet ken

\(\dfrac{22}{33}=\dfrac{22:11}{33:11}=\dfrac{2}{3}\)
Ta có: 
Mẫu số chung 2 phân số: 57
\(\dfrac{12}{19}=\dfrac{12*3}{19*3}=\dfrac{36}{57}\)
\(\dfrac{2}{3}=\dfrac{2*19}{3*19}=\dfrac{38}{57}\)
Vì \(36< 38\) nên\(\dfrac{36}{57}< \dfrac{38}{57}\)
Vậy \(\dfrac{12}{19}< \dfrac{22}{33}\)

\(\dfrac{22}{33}\)=\(\dfrac{22:11}{33:11}\)=\(\dfrac{2}{3}\)=\(\dfrac{2\times6}{3\times6}\)=\(\dfrac{12}{18}\)>\(\dfrac{12}{19}\)

Ta có :

\(\frac{33}{98}=\frac{33.25}{98.25}=\frac{825}{2450}\)

\(\frac{16}{50}=\frac{16.49}{50.49}=\frac{784}{2450}\)

Vì \(825>784\)nên \(\frac{825}{2450}>\frac{784}{2450}\)hay \(\frac{33}{98}>\frac{16}{50}\)

~ Hok tốt ~

Trả lời:

33/98>16/50(nếu sai bỏ qua cho mk  nha)

Bài 4: 

\(\left|x-3\right|=11\)

\(\Leftrightarrow\left[{}\begin{matrix}x-3=11\\x-3=-11\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=14\\x=-8\end{matrix}\right.\)