C = \(\left(\frac{1}{2}-1\right)+\left(1-\frac{3}{4}\right)+\left(\frac{7}{8}-1\right)+......+\left(1-\frac{1023}{1024}\right)\) ) . tính c
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YN
6 tháng 4 2019
\(a)\frac{\left(\frac{3}{10}-\frac{4}{15}-\frac{7}{20}\right).\frac{5}{19}}{\left(\frac{1}{14}+\frac{1}{7}-\frac{-3}{35}\right).\frac{-4}{3}}\)\(=\frac{\frac{-19}{60}.\frac{5}{19}}{\frac{3}{10}.\frac{-4}{3}}=\frac{5}{24}\)
Hok tốt
7 tháng 7 2021
\(\frac{1}{2.5}\)\(+\)\(\frac{1}{5.8}\)\(+\frac{1}{8.11}\)\(+...+\frac{1}{152.155}\)
=\(\frac{1}{2}\) \(-\frac{1}{5}\) \(+\frac{1}{5}\) \(-\frac{1}{8}\) \(+...+\frac{1}{152}\) \(-\frac{1}{155}\)
=\(\frac{1}{2}\)\(-\frac{1}{155}\)
=\(\frac{153}{310}\)
XO
7 tháng 7 2021
a) \(A=\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)\left(\frac{1}{4}-1\right)....\left(\frac{1}{1000}-1\right)=-\frac{1}{2}.\left(-\frac{2}{3}\right).\left(-\frac{3}{4}\right)...\left(-\frac{999}{1000}\right)\)
\(=-\frac{1.2.3...999}{2.3.4...1000}=-\frac{1}{1000}\)
b)\(B=\frac{\frac{3}{5}+\frac{3}{7}-\frac{3}{11}}{\frac{4}{5}+\frac{4}{7}-\frac{4}{11}}:\frac{3}{4}=\frac{3\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{11}\right)}{4\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{11}\right)}:\frac{3}{4}=\frac{3}{4}:\frac{3}{4}=1\)
d) \(D=1+\frac{1}{2}+\frac{1}{4}+..+\frac{1}{512}+\frac{1}{1024}\)
=> \(2D=2+1+\frac{1}{2}+...+\frac{1}{256}+\frac{1}{512}\)
=> \(2D-D=\left(2+1+\frac{1}{2}+...+\frac{1}{256}+\frac{1}{512}\right)-\left(1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{512}+\frac{1}{1024}\right)\)
=> \(D=2-\frac{1}{1024}=\frac{2047}{1024}\)
\(C=\left(\frac{1}{2}-1\right)+\left(1-\frac{3}{4}\right)+\left(\frac{7}{8}-1\right)+...+\left(1-\frac{1023}{1024}\right)\)
\(C=\left(\frac{1}{2^1}-\frac{2}{2}\right)+\left(\frac{2^2}{2^2}-\frac{3}{2^2}\right)+...+\left(\frac{1024}{1024}-\frac{1023}{2^{10}}\right)\)
\(C=\frac{-1}{2}+\frac{1}{2^2}-\frac{1}{2^3}+...+\frac{1}{2^{10}}\)
\(2C=-1+\frac{1}{2}-\frac{1}{2^2}+...+\frac{1}{2^9}\)
\(2C+C=\left(-1+\frac{1}{2}-\frac{1}{2^2}+...+\frac{1}{9}\right)+\left(-\frac{1}{2}+\frac{1}{2^2}-..+\frac{1}{2^{10}}\right)\)
\(3C=\frac{1}{2^{10}}-1\)
\(C=\frac{\frac{1}{2^{10}}-1}{3}\)
hok tốt!!