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A = - (1/4.5 + 1/5.6 + 1/6.7 + 1/7.8 + 1/8.9 +1/9.10)
A = -( 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8 + 1/8 - 1/9 + 1/9 - 1/10)
A = -( 1/4 - 1/10)
A = -3/20
B = 7(5/2.7 + 4/7.11 + 3/11.14 + 1/14.15 + 13/15.28)
B = 7(1/2 - 1/7 + 1/7 - 1/11 +......+ 1/15 - 1/28)
B = 7(1/2 - 1/28)
B = 7 . 13/28
B = 13/4
\(a,A=\frac{-1}{20}+\frac{-1}{30}+\frac{-1}{42}+\frac{-1}{56}+\frac{-1}{72}+\frac{-1}{90}\)
\(=\frac{-1}{4.5}+\frac{-1}{5.6}+\frac{-1}{6.7}+\frac{-1}{7.8}+\frac{-1}{8.9}+\frac{-1}{9.10}\)
\(=\frac{-1}{4}+\frac{1}{5}-\frac{1}{5}+\frac{1}{6}-...-\frac{1}{9}+\frac{1}{10}\)
\(=-\frac{1}{4}+\frac{1}{10}\)
\(=-\frac{3}{20}\)
\(b,B=\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}\)
\(\frac{B}{7}=\frac{5}{2.7}+\frac{4}{11.7}+\frac{3}{11.14}+\frac{1}{14.15}+\frac{13}{15.28}\)
\(=\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-....-\frac{1}{28}\)
\(=\frac{1}{2}-\frac{1}{28}=\frac{13}{28}\)
a) \(A=\frac{-1}{20}+\frac{-1}{30}+\frac{-1}{42}+\frac{-1}{56}+\frac{-1}{72}+\frac{-1}{90}\)
\(\Rightarrow-1.A=\frac{1}{20}+\frac{1}{30}+........+\frac{1}{90}\)
\(=\frac{1}{4.5}+\frac{1}{5.6}+........+\frac{1}{9.10}\)
\(=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+........+\frac{1}{9}-\frac{1}{10}=\frac{1}{4}-\frac{1}{10}=\frac{3}{20}\)
\(\Rightarrow A=\frac{3}{20}:\left(-1\right)=\frac{-3}{20}\)
b) \(B=\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}\)
\(\Rightarrow\frac{1}{7}B=\frac{5}{2.7}+\frac{4}{7.11}+\frac{3}{11.14}+\frac{1}{14.15}+\frac{13}{15.28}\)
\(=\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{15}+\frac{1}{15}-\frac{1}{28}\)
\(=\frac{1}{2}-\frac{1}{28}=\frac{13}{28}\)
\(\Rightarrow B=\frac{13}{28}:\frac{1}{7}=\frac{13}{28}.7=\frac{13}{4}\)
\(A=-\frac{1}{20}+-\frac{1}{30}+-\frac{1}{42}+...+-\frac{1}{90}\)
\(\Leftrightarrow A=\left(-1\right)\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(A=\left(-1\right)\left(\frac{1}{4}-\frac{1}{10}\right)\)
\(A=-\frac{3}{20}\)
a) A = \(\frac{1}{5}\) - \(\frac{1}{4}\)+ \(\frac{1}{6}\)- \(\frac{1}{5}\)+ \(\frac{1}{7}\)-\(\frac{1}{6}\)+\(\frac{1}{8}\)-\(\frac{1}{7}\)+\(\frac{1}{9}\)- \(\frac{1}{8}\)+ \(\frac{1}{10}\)- \(\frac{1}{9}\)
= \(\frac{-1}{4}\)+\(\frac{1}{10}\)= \(\frac{-6}{40}\)= \(\frac{-3}{20}\)
b) B = \(\frac{5}{2.1}\)+ \(\frac{1}{11}\)(4 + \(\frac{3}{2}\)) + \(\frac{1}{2.15}\)(1 + \(\frac{13}{2}\))
= \(\frac{5}{2.1}\)+ \(\frac{1}{11}\).\(\frac{11}{2}\)+ \(\frac{1}{2.15}\).\(\frac{15}{2}\)
= \(\frac{5}{2}\)+ \(\frac{1}{2}\)+ \(\frac{1}{4}\)= 3 + \(\frac{1}{4}\)= \(\frac{13}{4}\)
a,A=4/2.4+4/4.6+4/6.8+......+4/2012.2014
\(\Rightarrow\frac{1}{2}A=\frac{2}{2\cdot4}+\frac{2}{4\cdot6}+...+\frac{2}{2012\cdot2014}\)
\(\Rightarrow\frac{1}{2}A=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2012}-\frac{1}{2014}\)
\(\Rightarrow\frac{1}{2}A=\frac{1}{2}-\frac{1}{2014}\)
\(\Rightarrow A=1-\frac{1}{1007}\)
\(\Rightarrow A=\frac{1006}{1007}\)