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\(a.\)
\(\frac{15}{33}+\frac{7}{20}+\frac{18}{33}+\frac{13}{20}\)
\(=\left(\frac{15}{33}+\frac{18}{33}\right)+\left(\frac{13}{20}+\frac{7}{20}\right)\)
\(=\frac{33}{33}+\frac{20}{20}\)
\(=1+1=2\)
\(b.\)
\(2\frac{1}{2}+\frac{4}{7}:\left(-\frac{8}{21}\right)\)
\(=\frac{5}{2}+\frac{4}{7}:\left(-\frac{8}{21}\right)\)
\(=\frac{5}{2}+\frac{4}{7}.\left(-\frac{21}{8}\right)\)
\(=\frac{5}{2}+\frac{1}{1}.\left(-\frac{3}{2}\right)\)
\(=\frac{5}{2}-\frac{3}{2}\)
\(=1\)
\(c.\)
\(\left(-\frac{1}{2}\right)^3+\frac{1}{2}:5\)
\(=-\frac{1}{8}+\frac{1}{2}.\frac{1}{5}\)
\(=-\frac{1}{8}+\frac{1}{10}\)
\(=-\frac{1}{40}\)
a) \(\frac{15}{33}+\frac{7}{20}+\frac{18}{33}+\frac{13}{20}=\left(\frac{15}{33}+\frac{18}{33}\right)+\left(\frac{7}{20}+\frac{13}{20}\right)\) = 1 + 1 = 2
b) \(2\frac{1}{2}+\frac{4}{7}:\left(\frac{-8}{21}\right)=\frac{5}{2}+\frac{4}{7}:\left(\frac{-8}{21}\right)=\frac{5}{2}+\frac{-3}{2}\) = 1
c) \(\left(\frac{-1}{2}\right)\)3 + \(\frac{1}{2}\) : 5 = \(\frac{-1}{8}+\frac{1}{10}\) = \(\frac{-1}{40}\)
Chúc bạn học tốt!
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) \(C=\frac{4^{20}+4^{29}}{8^{13}+8^{15}}=\frac{\left(2^2\right)^{20}+\left(2^2\right)^{29}}{\left(2^3\right)^{13}+\left(2^3\right)^{15}}=\frac{2^{40}+2^{58}}{2^{39}+2^{45}}=\frac{2^{40}\left(1+2^{18}\right)}{2^{39}\left(1+2^6\right)}=\frac{2\left(1+2^{18}\right)}{1+2^6}=\frac{2+2^{19}}{1+2^6}\)
\(B=\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^{10}}\\ \Rightarrow2B=1+\frac{1}{2}+....=\frac{1}{2^9}\\ \Rightarrow B=1-\frac{1}{2^{10}}\)
\(C=\frac{4^{20}+4^{29}}{8^{13}+8^{15}}=\frac{\left(2^2\right)^{20}+\left(2^2\right)^{29}}{\left(2^3\right)^{13}+\left(2^3\right)^{15}}=\frac{2^{40}+2^{58}}{2^{39}+2^{45}}=\frac{2^{39}\left(2+2^{19}\right)}{2^{39}\left(1+2^6\right)}\)