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a) \(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}+\frac{1}{16}-\frac{1}{32}\)
\(=1-\frac{1}{32}=\frac{31}{32}\)
b) \(\frac{1}{2}.\frac{1}{2}+\frac{1}{2}.\frac{1}{3}+\frac{1}{3}.\frac{1}{4}+\frac{1}{4}.\frac{1}{5}+\frac{1}{5}.\frac{1}{6}\)\
\(=\frac{1}{4}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(\frac{1}{4}-\frac{1}{6}=\frac{1}{12}\)
a) =\(\frac{57}{100}+\frac{17}{15}.\frac{25}{68}-\frac{1141}{500}\)
= \(\frac{57}{100}+\frac{1}{3}.\frac{5}{4}-\frac{1141}{500}\)
= \(\frac{57}{100}+\frac{5}{12}-\frac{1141}{500}\)
= -\(\frac{1943}{1500}\)
"." là nhân
b) = \(\frac{28}{15}.\frac{3}{4}-\left(\frac{8}{15}+\frac{1}{4}\right).\frac{21}{47}\)
= \(\frac{7}{5}-\frac{47}{60}.\frac{21}{47}\)
= \(\frac{7}{5}-\frac{7}{20}\)
= \(\frac{28}{20}-\frac{7}{20}\)
= \(\frac{21}{20}\)
K nhé
\(a,=\left(-\frac{3}{7}+\frac{3}{7}\right)+\frac{5}{13}=0+\frac{5}{13}=\frac{5}{13}\)
\(b,=-\frac{5}{21}+\left(-\frac{2}{21}\right)+\frac{8}{24}=-\frac{1}{3}+\frac{1}{3}=0\)
\(c,=\left[-\frac{6}{11}+\frac{\left(-5\right)}{11}\right]+2=-1+2=1\)
\(d,=\frac{-1+\left(-15\right)}{32}+\frac{1}{2}=-\frac{1}{2}+\frac{1}{2}=0\)
a) \(\frac{-3}{7}+\frac{5}{13}+\frac{3}{7}\)
\(=\left(\frac{-3}{7}+\frac{3}{7}\right)+\frac{5}{13}\)
\(=0+\frac{5}{13}=\frac{5}{13}\)
b) \(\frac{-5}{21}+\frac{-2}{21}+\frac{8}{24}\)
\(=\frac{-7}{21}+\frac{1}{3}\)
\(=\frac{-1}{3}+\frac{1}{3}=0\)
c) \(\frac{-5}{11}+\left(\frac{-6}{11}+2\right)\)
\(=\frac{-5}{11}+\frac{-6}{11}+2\)
\(=\left(-1\right)+2=1\)
d) \(\left(\frac{-1}{32}+\frac{1}{2}\right)+\frac{-15}{32}\)
\(=\frac{-1}{32}+\frac{1}{2}+\frac{-15}{32}\)
\(=\left(\frac{-1}{32}+\frac{-15}{32}\right)+\frac{1}{2}\)
\(=\frac{-16}{32}+\frac{1}{2}\)
\(=\frac{-1}{2}+\frac{1}{2}=0\)
a) \(\frac{-3}{7}+\frac{15}{26}-\left(\frac{2}{13}-\frac{3}{7}\right)=\frac{-3}{7}+\frac{15}{26}-\frac{2}{13}+\frac{3}{7}=\left(\frac{-3}{7}+\frac{3}{7}\right)+\left(\frac{15}{26}-\frac{2}{13}\right)\)
\(=\frac{15-4}{26}=\frac{11}{26}\)
c) \(\frac{-11}{23}.\frac{6}{7}+\frac{8}{7}.\frac{-11}{23}-\frac{1}{23}=\frac{-11}{23}.\left(\frac{6}{7}+\frac{8}{7}\right)-\frac{1}{23}\)
\(=\frac{-11}{23}.2-\frac{1}{23}=\frac{-22-1}{23}=\frac{-23}{23}=-1\)
\(\frac{6}{13}-\frac{3}{26}=\frac{9}{26}\)
\(\frac{15}{12}+\frac{6}{24}=\frac{3}{2}\)
\(\frac{6}{13}-\frac{3}{26}=\frac{12}{26}-\frac{3}{26}=\frac{9}{26}\)
\(\frac{15}{12}+\frac{6}{24}=\frac{30}{24}+\frac{6}{24}=\frac{3}{2}\)
#)Giải :
Câu 1 :
Đặt \(A=\frac{1}{20}+\frac{1}{21}+\frac{1}{22}+...+\frac{1}{27}\)
\(\Rightarrow A>\frac{1}{27}+\frac{1}{27}+...+\frac{1}{27}\)( 8 số hạng )
\(\Rightarrow A>\frac{8}{27}=\frac{8}{27}\)
\(\Rightarrow A>\frac{8}{27}\)
#~Will~be~Pens~#
Câu 1:(trội)
Ta có:\(\frac{1}{20}+\frac{1}{21}+...+\frac{1}{27}>\frac{1}{27}+\frac{1}{27}+...+\frac{1}{27}=\frac{8}{27}\left(đpcm\right)\)
Câu 2:\(D=\frac{2^{25}.3^{15}+3^{15}.5.2^{26}}{2^{25}.3^{17}+3^{15}.2^{25}}=\frac{2^{25}3^{15}\left(1+5.2\right)}{2^{25}3^{15}\left(3^2+1\right)}=\frac{11}{10}\)