Nếu:
\(\dfrac{a}{b}< 1\Rightarrow\dfrac{a+n}{b+n}< 1\left(n\in N\right)\)
\(B=\dfrac{10^{20}+1}{10^{21}+1}< 1\)
\(B< \dfrac{10^{20}+1+9}{10^{21}+1+9}\Rightarrow B< \dfrac{10^{20}+10}{10^{21}+10}\Rightarrow B< \dfrac{10\left(10^{19}+1\right)}{10\left(10^{20}+1\right)}\Rightarrow B< \dfrac{10^{19}+1}{10^{20}+1}=A\)\(\Rightarrow B< A\)
2.Tính:
A=\(\left(\dfrac{1}{10}-1\right).\left(\dfrac{1}{11}-1\right)\left(\dfrac{1}{12}-1\right).....\left(\dfrac{1}{100}-1\right)\)
B=\(\left(1-\dfrac{1}{2^2}\right)\left(1-\dfrac{1}{3^2}\right)\left(1-\dfrac{1}{10^2}\right)\)
C=\(\left(\dfrac{7}{9}+1\right)\left(\dfrac{7}{20}+1\right)\left(\dfrac{7}{33}+1\right)...\left(\dfrac{7}{108080}+1\right)\)
D=\(\left(1-\dfrac{28}{10}\right)\left(1-\dfrac{52}{22}\right)\left(1-\dfrac{80}{36}\right)...\left(1-\dfrac{21808}{10900}\right)\)
bài 1 : so sánh phân số sau:
a) \(\dfrac{18}{91}\)và\(\dfrac{23}{114}\)
b)\(\dfrac{21}{52}\)và\(\dfrac{213}{523}\)
bài 2:so sánh
a)\(\dfrac{n}{n+1}\)và\(\dfrac{n+2}{n+3}\)
b)\(\dfrac{n}{n+3}\)và\(\dfrac{n-1}{n+4}\)
c)\(\dfrac{n}{2n+1}\)và \(\dfrac{3n+1}{6n+3}\)
bài 3: so sánh A và B
a)\(A=\dfrac{20}{39}+\dfrac{22}{27}+\dfrac{18}{43}\)
\(B=\dfrac{14}{39}+\dfrac{22}{29}+\dfrac{18}{14}\)
b)\(A=\dfrac{10^{1992}+1}{10^{1991}+1}\)
\(B=\dfrac{10^{1993}+1}{10^{1992}+1}\)
c)\(A=\dfrac{10^7+5}{10^7-8}\)
\(B=\dfrac{10^8+6}{10^8-7}\)
bài 1 : so sánh :
a) \(\dfrac{23}{21}\)và\(\dfrac{21}{23}\)
b)\(\dfrac{19}{26}\)và \(\dfrac{21}{25}\)
bài 2 : sắp sếp các phân số sau từ bé đến lớn :
a)\(\dfrac{7}{36};\dfrac{24}{36};\dfrac{13}{36};\dfrac{1}{36};\dfrac{43}{36};\dfrac{36}{36}\)
b)\(\dfrac{-3}{10};\dfrac{-31}{100};\dfrac{-297}{1000};\dfrac{10000}{-3056}\)
c)\(\dfrac{13}{20};\dfrac{7}{20};\dfrac{9}{4};\dfrac{2}{5};\dfrac{1}{2}\)
d)\(\dfrac{13}{21};\dfrac{152}{17};\dfrac{13}{17};\dfrac{-5}{21}\)
e)\(\dfrac{-1}{2};\dfrac{3}{-4};\dfrac{-2}{3};\dfrac{4}{-5}\)
Chứng minh rằng :
a) \(\dfrac{1}{2!}+\dfrac{1}{3!}+\dfrac{1}{4!}+...+\dfrac{1}{100!}< 1\)
b) \(\dfrac{9}{10!}+\dfrac{9}{11!}+\dfrac{9}{12!}+...+\dfrac{9}{1000!}< \dfrac{1}{9!}\)
Tìm x biết:
a) \(\dfrac{x+5}{3}\)=\(\dfrac{x-6}{7}\)
b) x - \(\dfrac{20}{11.13}\)-\(\dfrac{20}{13.15}\)-\(\dfrac{20}{15.17}\)-...-\(\dfrac{20}{53.55}\)=\(\dfrac{3}{11}\)
\(\dfrac{1}{3}\)+\(\dfrac{1}{6}\)+\(\dfrac{1}{10}\)+...+\(\dfrac{2}{n\left(n+1\right)}\)=\(\dfrac{2015}{2016}\)
So sánh:
A = \(\dfrac{20^{10}+1}{20^{10}-1}\)
B = \(\dfrac{20^{10}-1}{20^{10}-3}\)
Bài 1:
a) \(\left[\dfrac{3}{20}-\dfrac{1}{5}x\right].1\dfrac{2}{3}=1\dfrac{1}{4}\)
b)\(\dfrac{-2}{3}.x+\dfrac{1}{5}=\dfrac{3}{10}\)
c)\(\dfrac{-2}{3} \)-\(\dfrac{1}{3}\left(2x-7\right)=\dfrac{3}{2}\)
So sánh A và B :
a) \(A=\dfrac{20}{39}+\dfrac{22}{27}+\dfrac{18}{43}\)
\(B=\dfrac{14}{39}+\dfrac{22}{29}+\dfrac{18}{41}\)
b) \(A=\dfrac{3}{8^3}+\dfrac{7}{8^4}\)
\(B=\dfrac{7}{8^3}+\dfrac{3}{8^4}\)
c) \(A=\dfrac{10^7+5}{10^7-8}\)
\(B=\dfrac{10^8+6}{10^8-7}\)
d) \(A=\dfrac{10^{1992}+1}{10^{1991}+1}\)
\(B=\dfrac{10^{1993}+1}{10^{1992}+1}\)
Chứng minh rằng:
1) B =\(\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}+...+\dfrac{1}{19}>1\)
2) \(A=\dfrac{1}{5}+\dfrac{2}{5^2}+\dfrac{3}{5^3}+\dfrac{4}{5^4}+...+\dfrac{500}{5^{500}}<100\)
3) \(C=\dfrac{1}{2^3}+\dfrac{1}{3^3}+\dfrac{1}{4^3}+\dfrac{1}{5^3}+...+\dfrac{1}{500^3}<\dfrac{1}{4}\)
4) \(D=\dfrac{4}{3}+\dfrac{10}{9}+\dfrac{28}{27}+...+\dfrac{3^{98}+1}{3^{98}}<100\)
Làm giúp mình sớm nha! Thanks.
