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\(C=\frac{1.4}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}.....\frac{2013.2016}{2014.2015}\)
\(C=\frac{\left(1.2.3.....2013\right).\left(4.5.6.....2016\right)}{\left(2.3.4.....2014\right).\left(3.4.5.....2015\right)}\)
\(C=\frac{1}{2014}.\frac{2016}{3}\)
\(C=\frac{336}{1007}\)
\(\frac{1.4}{2.3}\)x\(\frac{2.5}{3.4}\)x\(\frac{3.6}{4.5}\)x.........x\(\frac{2013.2016}{2014.2015}\)=\(\frac{1.2.3....2013}{2.3.4...2014}\)x \(\frac{4.5.6....2016}{3.4.5....2015}\)
=\(\frac{1}{2014}\)x \(\frac{2016}{3}\)
=\(\frac{2016}{6042}\)= \(\frac{336}{1007}\)
\(A=\frac{5.2^{30}.3^{18}-2^2.3^{20}.2^{27}}{5.2^9.6^{19}-7.2^{29}.3^{18}}\)
\(A=\frac{5.2^{30}.3^{18}-2^{29}.3^{20}}{5.2^9.2^{19}.3^{19}-7.2^{29}.3^{18}}\)
\(A=\frac{5.2^{30}.3^{18}-2^{29}.3^{20}}{5.2^{28}.3^{19}-7.2^{29}.3^{18}}\)
\(A=\frac{2^{29}.3^{18}.\left(5.2.1-9\right)}{2^{28}.3^{18}.\left(5.1.3-7.2.1\right)}\)
\(A=\frac{2.1}{1}=2\)
\(\frac{1}{9.10}-\frac{1}{8.9}-\frac{1}{7.8}-\frac{1}{6.7}-\frac{1}{5.6}-\frac{1}{4.5}-\frac{1}{3.4}-\frac{1}{2.3}-\frac{1}{1.2}\)
\(=-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}\right)+\frac{1}{9.10}\)
\(=-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{8}-\frac{1}{9}\right)+\frac{1}{90}\)
\(=-\left(1-\frac{1}{10}\right)+\frac{1}{90}\)
\(=-\frac{9}{10}+\frac{1}{90}\)
= ...
bn tự tính nha!
Bằng -30
HT