Ta có : A <1 .Nếu \(\frac{a}{b}\) <1 thì \(\frac{a+m}{b+m}\)>\(\frac{a}{b}\)với (m>0)
Vậy A = \(\frac{10^{11}-1}{10^{12}-1}\)< \(\frac{\left(10^{11}-1\right)+11}{\left(10^{12}-1\right)+11}\)=\(\frac{10^{11}+10}{10^{12}+10}\)
\(\Rightarrow\)A < \(\frac{10.\left(10^{10}+1\right)}{10.\left(10^{11}+1\right)}\)=\(\frac{10^{10}+1}{10^{11}+1}\)=B
Do đố : A<B
Duyệt nha !!! Chúc bn hk giỏi !!!
So sánh A và B:
a) A = \(\frac{10^{19}+1}{10^{20}+1}\); B = \(\frac{10^{20}+1}{10^{21}+1}\)
b) A = \(\frac{9^{99}+1}{9^{100}+1}\); B = \(\frac{10^{98}-1}{10^{99}-1}\)
Bài 1: rút gọn các phân số sau:
a) \(\frac{3^{10}.\left(-5\right)^{21}}{\left(-5\right)^{20}.3^{12}}\)
b) \(\frac{-11^5.13^7}{11^5.13^8}\)
c) \(\frac{2^{10}.3^{10}-2^{10}.3^9}{2^9.3^{10}}\)
d) \(\frac{5^{11}.7^{12}+5^{11}.7^{11}}{5^{12}.7^{12}+9.5^{11}.7^{11}}\)
Bài 2 so sánh
a) A= \(\frac{10^{1993}+10}{10^{1993}+1}\)và B= \(\frac{10^{1994}+10}{10^{1994}+1}\)
Cho: A =\(\frac{10^{2001}+1}{10^{2002}+1}\)
và B=\(^{\frac{10^{2002}+_{ }1}{10^{2003}+1}}\)
So sánh A và B
ĐỀ : Cho \(A=\dfrac{1.0^{11}-1}{10^{12}-1}\); \(B=\dfrac{10^{10}+1}{10^{10}+1}\)
So sánh A và B .
\(\frac{10+\frac{9}{2}+\frac{8}{3}+\frac{7}{4}+ \frac{6}{5}+\frac{5}{6}+\frac{4}{7}+\frac{3}{8}+\frac{2}{9}+\frac{1}{10}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{10}+\frac{1}{11}}\)
Bài 1:So sánh Avà B biết rằng:
A=\(\frac{10^{15}+1}{10^{16}+1};\) B=\(\frac{10^{16}+1}{10^{17}+1}\)
A=\(\frac{3}{8^3}+\frac{7}{8^4}\); B=\(\frac{7}{8^3}+\frac{3}{8^4}\)
A=\(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+.......+\frac{1}{19}+\frac{1}{20};\) B=\(\frac{1}{2}\)
Bài 2:Dạng tính tổng đặc biệt:
\(A=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+.....+\frac{1}{99\cdot100}\)
\(B=\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+.....+\frac{2}{99\cdot101}\)
\(C=\frac{3^2}{10}+\frac{3^2}{40}+\frac{3^2}{88}+......+\frac{3^2}{340}\)
\(D=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+......+\frac{1}{3^8}\)
\(E=\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right).......\left(1-\frac{1}{99}\right)\)
Bài 3:Dạng chứng minh:
\(A=1+\frac{1}{2}+\frac{1}{3}+......+\frac{1}{99}.\)Chứng minh rằng A chia hết cho 100
A=\(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{70}\).Chứng minh rằng A>\(\frac{4}{3}\)
1.so sánh
a. A=\(\frac{2005^{2005}+1}{2005^{2006}+1}\) và B=\(\frac{2005^{2004}+1}{2005^{2005}+1}\)
b. A=\(\frac{20^{10}+1}{20^{10}-1}\) và B=\(\frac{20^{10}-1}{20^{10}-3}\)
c. A=\(\frac{2009^{2009}+1}{2009^{2010}+1}\) và B=\(\frac{2009^{2010}+2}{2009^{2011}-2}\)
d. A=\(\frac{2013^{2014}+2014}{2013^{2014}-2014}\) và B=\(\frac{2013^{2014}-2014}{2013^{2014}-6042}\)
CMR: \(\frac{9}{10!}+\frac{9}{11!}+\frac{9}{12!}+...+\frac{9}{1000!}< \frac{1}{9!}\)
