tính:
B=\(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+........+\frac{1}{2^{10}}\)
C=\(\frac{4^{20}+4^{29}}{8^{13}+8^{15}}\)
K
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29 tháng 6 2022
a: \(=\left(-\dfrac{25}{140}+\dfrac{245}{140}+\dfrac{32}{140}\right)\cdot\dfrac{-69}{20}\)
\(=\dfrac{252}{140}\cdot\dfrac{-69}{20}\)
\(=\dfrac{9}{5}\cdot\dfrac{-69}{20}=\dfrac{-621}{100}\)
b: \(=\left(6-2-\dfrac{4}{5}\right)\cdot\dfrac{25}{8}-\dfrac{8}{5}\cdot4\)
\(=\dfrac{16}{5}\cdot\dfrac{25}{8}-\dfrac{32}{5}=\dfrac{18}{5}\)
c: \(=\left(\dfrac{2}{24}+\dfrac{18}{24}+\dfrac{14}{24}\right):\dfrac{-17}{8}\)
\(=\dfrac{34}{24}\cdot\dfrac{-8}{17}=\dfrac{-1}{3}\cdot2=-\dfrac{2}{3}\)
PL
20 tháng 5 2017
\(A=-1-4=-5\)
\(B=\frac{4}{3}.\frac{15}{7}-16\)
\(B=\frac{20}{7}-16\)
\(B=\frac{-92}{7}\)
\(C=\frac{28}{15}.0,25.3+\left(\frac{8}{15}-\frac{1}{4}\right)\div1\frac{23}{24}\)
\(C=1,4+\frac{17}{60}\div\frac{47}{24}\)
\(C=1,4+\frac{34}{235}\)
\(C=\frac{363}{235}\)
20 tháng 5 2017
\(A=\frac{-15}{8}+\frac{7}{8}-4\)
\(=-1-4=-5\)
\(B=\left(4-2\frac{2}{3}\right).2\frac{1}{7}-1\frac{3}{5}:\frac{1}{10}\)
\(=\frac{4}{3}.\frac{15}{7}-\frac{8}{5}:\frac{1}{10}\)
\(=\frac{20}{7}-16=\frac{-92}{7}\)
\(C=1\frac{13}{15}.\left(0,5\right)^2.3+\left(\frac{8}{15}-25\%\right):1\frac{23}{24}\)
\(=\frac{28}{15}.\frac{1}{4}.3+\frac{17}{60}:\frac{47}{24}\)
\(=\frac{7}{15}.3+\frac{17}{60}:\frac{47}{24}\)
\(=\frac{7}{5}+\frac{34}{235}=\frac{363}{235}\)
b) \(B=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}\)
\(\Rightarrow2B=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\)
\(\Rightarrow2B-B=\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}\right)\)
\(\Rightarrow B=1-\frac{1}{2^9}\)
c) \(C=\frac{4^{20}+4^{29}}{8^{13}+8^{15}}=\frac{\left(2^2\right)^{20}+\left(2^2\right)^{29}}{\left(2^3\right)^{13}+\left(2^3\right)^{15}}=\frac{2^{40}+2^{58}}{2^{39}+2^{45}}=\frac{2^{40}\left(1+2^{18}\right)}{2^{39}\left(1+2^6\right)}=\frac{2\left(1+2^{18}\right)}{1+2^6}=\frac{2+2^{19}}{1+2^6}\)
\(B=\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^{10}}\\ \Rightarrow2B=1+\frac{1}{2}+....=\frac{1}{2^9}\\ \Rightarrow B=1-\frac{1}{2^{10}}\)
\(C=\frac{4^{20}+4^{29}}{8^{13}+8^{15}}=\frac{\left(2^2\right)^{20}+\left(2^2\right)^{29}}{\left(2^3\right)^{13}+\left(2^3\right)^{15}}=\frac{2^{40}+2^{58}}{2^{39}+2^{45}}=\frac{2^{39}\left(2+2^{19}\right)}{2^{39}\left(1+2^6\right)}\)