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Tình hợp lí
C=(11213.20 +11220.27 +11227.34 +...+11262.69 ):(−59.13 −79.25 −1319.25 −3119.69 )
7/1.3 + 7/3.5 + 7/5.7 + ... + 7/99.101
= 7.(1/1.3 + 1/3.5 + 1/5.7 + ... + 1/99.101)
= 7/2 . 2 . (1/1.3 + 1/3.5 + 1/5.7 + ... + 1/99.101)
= 7/2 . (2/1.3 + 2/3.5 + 2/5.7 + ... + 2/99.101)
= 7/2 . (1 - 1/3 + 1/3 - 1/5 + ... + 1/99 - 1/101)
= 7/2 . (1 - 1/101)
= 7/2 . 100/101
= 350/101
\(\frac{7}{1.3}+\frac{7}{3.5}+...+\frac{7}{99.101}\)
\(=7\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{99.101}\right)\)
\(=\)\(\frac{7}{2}.2.\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{99.101}\right)\)
\(=\)\(\frac{7}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{99.101}\right)\)
Ta có :\(\frac{-17,5+\frac{5}{3}-2\frac{1}{7}}{7-\frac{2}{3}+\frac{6}{7}}=\frac{-17,5+\frac{5}{3}-\frac{15}{7}}{7-\frac{2}{3}+\frac{6}{7}}=\frac{-2,5\left(.7-\frac{2}{3}+\frac{6}{7}\right)}{7-\frac{2}{3}+\frac{6}{7}}=-2,5\)
C=\(\frac{-17,5+\frac{5}{3}-2\frac{1}{7}}{7,0-\frac{2}{3}+\frac{6}{7}}\)
=\(\frac{\frac{-367,5}{21}+\frac{35}{21}-\frac{45}{21}}{\frac{147}{21}-\frac{14}{21}+\frac{18}{21}}\)
=\(\frac{\frac{-377,5}{21}}{\frac{151}{21}}\)
=\(-\frac{5}{2}\)
\(TA-CO':\)
\(A=\frac{4+\frac{7}{2014}-\frac{7}{2015}+\frac{7}{2012}-\frac{7}{2013}}{7+\frac{7}{2014}-\frac{7}{2015}+\frac{7}{2012}-\frac{7}{2013}}\)
\(A=\frac{4\left(\frac{1}{2014}-\frac{1}{2015}+\frac{1}{2012}-\frac{1}{2013}\right)}{7\left(\frac{1}{2014}-\frac{1}{2015}+\frac{1}{2012}-\frac{1}{2013}\right)}\)
\(A=\frac{4}{7}\)
\(B=\frac{1+2+...+2^{2013}}{2^{2015}-2}\)
ĐẶT \(C=1+2+...+2^{2013}\)
\(\Rightarrow2C=2+2^2+...+2^{2014}\)
\(\Rightarrow2C-C=\left(2+2^2+...+2^{2014}\right)-\left(1+2+...+2^{2013}\right)\)
\(\Rightarrow C=2^{2014}-2\)
\(\Rightarrow B=\frac{2^{2014}-1}{2^{2015}-2}\)
\(B=\frac{2^{2014}-1}{2\left(2^{2014}-1\right)}\)
\(B=\frac{1}{2}\)
\(\Rightarrow A-B=\frac{3}{7}-\frac{1}{2}=\frac{6}{14}-\frac{7}{14}\)
\(A-B=\frac{6-7}{14}=\frac{-1}{14}\)
VẬY, \(A-B=\frac{-1}{14}\)
A) \(\frac{1}{2}\cdot\left(\frac{2}{9}+\frac{3}{7}-\frac{5}{27}\right)\)
\(=\frac{1}{2}\cdot\frac{1}{2}\)
\(=\frac{1}{4}\)
B) \(\left(\frac{-5}{28}+1.75+\frac{8}{35}\right):\left(-3\frac{9}{20}\right)\)
\(=\left(\frac{-5}{28}+\frac{7}{4}+\frac{8}{35}\right):\frac{-69}{20}\)
\(=\frac{14}{5}:\frac{-69}{20}\)
\(=\frac{-56}{69}\)
=\(\frac{2}{7}.\left(\frac{22}{19}-\frac{3}{19}-\frac{15}{21}-\frac{6}{21}\right)\)
=\(\frac{2}{7}.\left(\frac{19}{19}-\frac{21}{21}\right)\)
=\(\frac{2}{7}.\left(1-1\right)=0\)
\(=\frac{2}{7}\left(\frac{22}{19}-\frac{15}{21}+\frac{-3}{19}+\frac{-6}{21}\right)\)
\(=\frac{2}{7}\left[\left(\frac{22}{19}-\frac{3}{19}\right)-\left(\frac{15}{21}+\frac{6}{21}\right)\right]\)
\(=\frac{2}{7}\left[1-1\right]=0\)
\(B=\frac{1}{7}\left(\frac{7}{6\cdot13}+\frac{7}{13\cdot20}+...+\frac{7}{293\cdot300}\right)\)
\(B=\frac{1}{7}\left(\frac{1}{6}-\frac{1}{13}+\frac{1}{13}-\frac{1}{20}+...+\frac{1}{293}-\frac{1}{300}\right)\)
\(B=\frac{1}{7}\left(\frac{1}{6}-\frac{1}{300}\right)=\frac{1}{7}\cdot\frac{49}{300}=\frac{7}{300}\)
Ta có : \(B=\frac{7^2}{6.13}+\frac{7^2}{13.20}+\frac{7^2}{20.27}+......+\frac{7^2}{293.300}\)
\(=7.\left(\frac{7}{6.13}+\frac{7}{13.20}+\frac{7}{20.27}+......+\frac{7}{293.300}\right)\)
\(=7.\left(\frac{1}{6}-\frac{1}{13}+\frac{1}{13}-\frac{1}{20}+.......+\frac{1}{293}-\frac{1}{300}\right)\)
\(=7\left(\frac{1}{6}-\frac{1}{300}\right)\)
\(=7.\frac{49}{300}=\frac{343}{300}\)