Ta có : các phân số từ 1/11 ; 1/12  đến  1/19 đều lớn hơn phân số 1/20

Từ đó lại có : 1/11 + 1/12 + 1/13 + ... + 1/19 + 1/20 > 1/20 + 1/20 + 1/20+ ...+ 1/20 (  số số hạng gồm 10 phân số 1/20)

=> 1/11+ 1/12+ 1/13+...+ 1/20 > 10/20

=>  1/11+1/12+1/13+...+1/20  > 1/2

<=>    S   > 1/2 .

Ta có : 

\(S=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}+\frac{1}{17}+\frac{1}{18}+\frac{1}{19}+\frac{1}{20}>\frac{1}{20}+\frac{1}{20}+...+\frac{1}{20}\) ( 10 số \(\frac{1}{20}\) )

\(S>\frac{1}{20}.10=\frac{10}{20}=\frac{1}{2}\)

Vậy \(S>\frac{1}{2}\)

\(A=\frac{4}{a-1}+\frac{b}{a-1}=\frac{b+4}{a-1}\)

\(A=\frac{b+4}{a-1}\)

\(A=\frac{a-1+b-a+5}{a-1}\)

\(A=\frac{b-a+5}{a-1}\)

......

a) \(\frac{a}{b}=\frac{36}{45}=\frac{4}{5}\)

\(\RightarrowƯCLN=\frac{a}{4}\).

Mà BCNN = \(\frac{ab}{ƯCLN}\)

\(\Rightarrow300=\frac{ab}{\left(\frac{a}{4}\right)}\) 

Suy ra b = 75

Suy ra a = 60 

b với c tương tự nha bn!!!

Theo bài ra , ta có : 

2135 =35 =ab mà UCLN(a,b) = 30 

=) ab =35 =3×305×30 =90150 

Vậy phân số mới là 90150  

Ta có : 

\(\frac{1^2}{1.2}.\frac{2^2}{2.3}.\frac{3^2}{3.4}.....\frac{99^2}{99.100}\)

\(=\)\(\frac{1^2.2^2.3^2.....99^2}{1.2.2.3.3.4.....99.100}\)

\(=\)\(\frac{1^2.2^2.3^2.....99^2}{1^2.2^2.3^2.4^2.....99^2}.\frac{1}{100}\)

\(=\)\(\frac{1}{100}\)

Ta có: \(\frac{9}{21}=\frac{9:3}{21:3}=\frac{3}{7}\)

Và       \(\frac{-10}{15}=\frac{-10:5}{15:5}=-\frac{2}{3}\)

\(\Rightarrow\frac{9}{21}+\frac{-10}{15}=\frac{3}{7}+\frac{-2}{3}=\frac{9}{21}+\frac{-14}{21}=\frac{9+\left(-14\right)}{21}=\frac{-5}{21}\)

Tương tự: \(\frac{24}{56}=\frac{24:8}{56:8}=\frac{3}{7}\)

Và \(\frac{-18}{27}=\frac{-18:9}{27:9}=\frac{-2}{3}\)

\(\Rightarrow\frac{24}{56}+\frac{-18}{27}=\frac{3}{7}+\frac{-2}{3}=\frac{-5}{21}\)

\(\frac{3}{7}+\frac{-2}{3}=\frac{9}{21}-\frac{14}{21}=\frac{-5}{21}\)

\(\frac{9}{21}+\frac{-10}{15}=\frac{3}{7}-\frac{2}{3}=\frac{-5}{21}\)

\(\frac{24}{56}+\frac{-18}{27}=\frac{3}{7}-\frac{2}{3}=\frac{-5}{21}\)

\(\frac{-5}{12}+\frac{-1}{4}=\frac{-5}{12}+\frac{-3}{12}=\frac{-5+-3}{12}=\frac{-8}{12}=\frac{-2}{3}\)

\(\frac{5}{12}+\frac{-3}{28}=\frac{35}{84}+\frac{-9}{84}=\frac{35+\left(-9\right)}{84}=\frac{26}{84}=\frac{13}{42}\)

\(\frac{-7}{15}+\frac{3}{35}=\frac{-49}{105}+\frac{9}{105}=\frac{-49+9}{105}=\frac{-40}{105}=\frac{-8}{21}\)

\(\frac{-5}{7}+\frac{-3}{4}=\frac{-20}{28}+\frac{-21}{28}=\frac{-20+\left(-21\right)}{28}=\frac{-41}{28}\)

\(\frac{-24}{54}+\frac{35}{-126}=\frac{-4}{9}+\frac{-5}{18}=\frac{-8}{18}+\frac{-5}{18}=\frac{-8+-5}{18}=\frac{-13}{18}\)

\(-\frac{3}{27}+\frac{56}{88}=\frac{-1}{9}+\frac{7}{11}=\frac{-11}{99}+\frac{63}{99}=\frac{-11+63}{99}=\frac{52}{99}\)