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8 tháng 5 2017

\(\Rightarrow A=\frac{5.2.3}{3.3.5.5}=\frac{1.2.1}{1.3.1.5}=\frac{2}{15}\)

     \(B=\frac{3.3.2.2-3.3.2}{2.2.2.3.3+7.3.3}=\frac{1.1.1.1-1.1.2}{2.1.1.1.1+7.1.1}=\frac{-1}{9}\)

=> A > B

Ai thấy đúng k nha

8 tháng 5 2017

\(A=\frac{5.6}{9.25}=\frac{1.2}{3.5}=\frac{2}{15}.\)

\(B=\frac{18.4-18}{8.9+7.9}=\frac{18\left(4-1\right)}{9\left(8+7\right)}=\frac{18.3}{9.15}=\frac{2.1}{15}=\frac{2}{15}.\)

\(\Rightarrow A=B.\)

8 tháng 6 2017

\(a,A=\dfrac{1}{7.9}\)\(B=\dfrac{1}{7}-\dfrac{1}{9}\)
\(\Leftrightarrow2A=\dfrac{2}{7.9}=\dfrac{1}{7}-\dfrac{1}{9}\)
\(2A=B\left(=\dfrac{1}{7}-\dfrac{1}{9}\right)\)
\(\Leftrightarrow A< B\)
\(b,A=\dfrac{15}{301}\)\(B=\dfrac{25}{499}\)
Ta thấy: \(\dfrac{15}{301}< \dfrac{15}{300}\)\(\dfrac{25}{499}>\dfrac{25}{500}\)
\(\dfrac{15}{300}=\dfrac{1}{20}\)\(\dfrac{25}{500}=\dfrac{1}{20}\)
\(\dfrac{1}{20}=\dfrac{1}{20}\Leftrightarrow\dfrac{15}{300}=\dfrac{25}{500}\)
\(\Leftrightarrow\dfrac{15}{301}< \dfrac{1}{20}< \dfrac{25}{499}\)
\(\Leftrightarrow\dfrac{15}{301}< \dfrac{25}{499}\)
\(\Leftrightarrow A< B\)
\(c,A=\dfrac{5.6}{9.25}\)\(B=\dfrac{18.4-18}{8.9+7.9}\)
\(A=\dfrac{5.6}{9.25}=\dfrac{1.2}{3.5}=\dfrac{2}{15}\)
\(B=\dfrac{18.4-18}{8.9+7.9}=\dfrac{18\left(4-1\right)}{9\left(8+7\right)}=\dfrac{18.3}{9.15}=\dfrac{2.1}{1.5}=\dfrac{2}{5}\)
\(\dfrac{2}{15}< \dfrac{2}{5}\)
\(\Leftrightarrow A< B\)
Chúc bạn học tốt!

8 tháng 6 2017

\(A< B\) mà. Cách trên khó hiểu chút. Theo cách này đi.
\(B=\dfrac{1}{7}-\dfrac{1}{9}\)
\(\Leftrightarrow B=\dfrac{2}{7.9}\)
\(\dfrac{1}{7.9}< \dfrac{2}{7.9}\)
\(\Leftrightarrow A< B\)

1: \(B=\dfrac{1}{7}-\dfrac{1}{9}=\dfrac{2}{63}>\dfrac{1}{7\cdot9}=A\)

2: \(A=\dfrac{15}{301}< \dfrac{15}{300}=\dfrac{1}{20}=\dfrac{25}{500}< \dfrac{25}{499}\)

 

giúp mik vs mik cần gấp 

10 tháng 3 2017

VIẾT HẲN PS RA CHỨ KO HIỂU

2 tháng 5 2016

A = \(\frac{5}{1.2}\) + \(\frac{5}{2.3}\) +........+\(\frac{5}{99.100}\) 

A = 5.(\(\frac{1}{1.2}\) + \(\frac{1}{2.3}\) +......+\(\frac{1}{99.100}\) )

A = 5. ( \(\frac{1}{1}\) - \(\frac{1}{2}\) +\(\frac{1}{2}-\frac{1}{3}\) +......+\(\frac{1}{99}-\frac{1}{100}\) )

A= 5. (\(1-\frac{1}{100}\))

A= 5.\(\frac{99}{100}\)

A= \(\frac{99}{20}\)

23 tháng 3 2017

B = \(\frac{1}{2.3}\)\(\frac{1}{3.4}\)+............+ \(\frac{1}{9.10}\)

    = \(\frac{1}{2}\)-  \(\frac{1}{3}\)+\(\frac{1}{3}\)-   \(\frac{1}{4}\)+ ...................+\(\frac{1}{9}\)-     \(\frac{1}{10}\)

    =  \(\frac{1}{2}\) -     \(\frac{1}{10}\)

     =       \(\frac{2}{5}\)

23 tháng 6 2015

\(A=\frac{5}{1.2}+\frac{5}{2.3}+\frac{5}{3.4}+...+\frac{5}{99.100}\)

\(A=5\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\right)\)

\(A=5\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\right)\)

\(A=5\left(1-\frac{1}{100}\right)\)

\(A=5.\frac{99}{100}\)

\(A=\frac{99}{20}\)

 

\(B=\frac{1}{1.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\)

\(B=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)

\(B=\frac{1}{2}-\frac{1}{10}\)

\(B=\frac{2}{5}\)

 

\(C=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}\)

\(C=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\)

\(C=\frac{1}{3}-\frac{1}{15}\)

\(C=\frac{4}{15}\)

23 tháng 6 2015

\(A=\frac{5}{1.2}+\frac{5}{2.3}+\frac{5}{3.4}+...+\frac{5}{99.100}\)

\(A=5\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\right)\)

\(A=5\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\right)\)

\(A=5\left(1-\frac{1}{100}\right)\)

\(A=5.\frac{99}{100}\)

\(A=\frac{99}{20}\)

 

\(B=\frac{1}{1.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\)

\(B=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)

\(B=\frac{1}{2}-\frac{1}{10}\)

\(B=\frac{2}{5}\)

 

\(C=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}\)

\(C=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\)

\(C=\frac{1}{3}-\frac{1}{15}\)

\(C=\frac{4}{15}\)

8 tháng 5 2017

\(A=\frac{1}{7\cdot9}\)

\(B=\frac{1}{7}-\frac{1}{9}\)

\(2A=\frac{1}{7}-\frac{1}{9}\)

\(\Rightarrow A< B\)

2A = 2 / 7.9

2A = 1/7 - 1/9

=> A < B

4 tháng 6 2016

Ta có:

\(A=\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+...+\frac{1}{9.10}\)

\(\Rightarrow A=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{9}-\frac{1}{10}\)

\(\Rightarrow A=\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{9}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{10}\right)\)

\(\Rightarrow A=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{9}+\frac{1}{10}\right)-2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{10}\right)\)

\(\Rightarrow A=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{9}+\frac{1}{10}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)\)

\(\Rightarrow A=\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}\)

\(\Rightarrow A=\left(\frac{1}{6}+\frac{1}{10}\right)+\left(\frac{1}{7}+\frac{1}{9}\right)+\frac{1}{8}\)

\(\Rightarrow A=\left(\frac{10}{6.10}+\frac{6}{6.10}\right)+\left(\frac{9}{7.9}+\frac{7}{7.9}\right)+\frac{8}{8.8}\)

\(\Rightarrow A=\frac{16}{6.10}+\frac{16}{7.9}+\frac{8}{8.8}\)

\(\Rightarrow A=8\left(\frac{2}{6.10}+\frac{2}{7.9}+\frac{1}{8.8}\right)\)

Ta lại có:

\(B=\frac{1}{6.10}+\frac{1}{7.9}+\frac{1}{8.8}+\frac{1}{9.7}+\frac{1}{10.6}\)

\(\Rightarrow B=\left(\frac{1}{6.10}+\frac{1}{6.10}\right)+\left(\frac{1}{7.9}+\frac{1}{7.9}\right)+\frac{1}{8.8}\)

\(\Rightarrow B=\frac{2}{6.10}+\frac{2}{7.9}+\frac{1}{8.8}\)

Vậy : 

\(A:B=8\left(\frac{2}{6.10}+\frac{2}{7.9}+\frac{1}{8.8}\right):\left(\frac{2}{6.10}+\frac{2}{7.9}+\frac{1}{8.8}\right)=8\)

Vậy \(A:B=8\)

12 tháng 7 2018

a/ 1/1.3 + 1/3.4+ .... + 1/9.10

= 1–1/3+1/3–1/4+1/4–1/5+...+1/8–1/9+1/9–1/10

=1–1/10

=10/10–1/10

=9/10