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\(\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{19.20}\)
\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{20}\)
\(=\frac{1}{5}-\frac{1}{20}\)
\(=\frac{4}{20}-\frac{1}{20}=\frac{3}{20}\)
C=\(\frac{7}{3.4}\)-\(\frac{9}{4.5}\)+\(\frac{11}{5.6}\)+\(\frac{13}{6.7}\)+\(\frac{15}{7.8}\)-\(\frac{17}{8.9}\)+\(\frac{19}{9.10}\)
=\(\frac{1}{3}\)+\(\frac{1}{4}\)-\(\frac{1}{4}\)-\(\frac{1}{5}\)+\(\frac{1}{5}\)+\(\frac{1}{6}\)-\(\frac{1}{6}\)-\(\frac{1}{7}\)+\(\frac{1}{7}\)+\(\frac{1}{8}\)-\(\frac{1}{8}\)-\(\frac{1}{9}\)+\(\frac{1}{9}\)+\(\frac{1}{10}\)
=\(\frac{1}{3}\)+\(\frac{1}{10}\)=\(\frac{13}{30}\)
B = \(\dfrac{1}{3.4}\) - \(\dfrac{1}{4.5}\) - \(\dfrac{1}{5.6}\) - \(\dfrac{1}{6.7}\) - \(\dfrac{1}{7.8}\) - \(\dfrac{1}{8.9}\) - \(\dfrac{1}{9.10}\)
B = \(\dfrac{1}{12}\) - ( \(\dfrac{1}{4.5}\) + \(\dfrac{1}{5.6}\) + \(\dfrac{1}{6.7}\) + \(\dfrac{1}{7.8}\) + \(\dfrac{1}{8.9}\) + \(\dfrac{1}{9.10}\))
B = \(\dfrac{1}{12}\) - ( \(\dfrac{1}{4}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{6}\) + \(\dfrac{1}{6}\) - \(\dfrac{1}{7}\) + \(\dfrac{1}{7}\) - \(\dfrac{1}{8}\) + \(\dfrac{1}{8}\) - \(\dfrac{1}{9}\) + \(\dfrac{1}{9}\) - \(\dfrac{1}{10}\))
B = \(\dfrac{1}{12}\) - ( \(\dfrac{1}{4}\) - \(\dfrac{1}{10}\))
B = \(\dfrac{1}{12}\) - \(\dfrac{3}{20}\)
B = - \(\dfrac{1}{15}\)
1/1.2 + 1/2.3 + 1/3.4 + ... + 1/49.50
= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/49 - 1/50
= 1 - 1/50
= 49/50
ỦNG HỘ NHA
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)
\(=1-\frac{1}{50}=\frac{49}{50}\)
\(A=\frac{4}{4.5}+\frac{4}{5.6}+\frac{4}{6.7}+...+\frac{4}{47.48}\)
\(A=4.\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+......+\frac{1}{47.48}\right)\)
\(A=4.\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+.....+\frac{1}{47}-\frac{1}{48}\right)\)
\(A=4.\left(\frac{1}{4}-\frac{1}{48}\right)\)
\(A=4.\frac{11}{48}\)
\(A=\frac{11}{12}\)
\(A=\frac{1}{1.2}+\frac{1}{2.3}+.......+\frac{1}{49.50}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+............+\frac{1}{49}-\frac{1}{50}\)
\(=1-\frac{1}{50}\)
\(=\frac{49}{50}\)
A=\(\frac{1}{1.2}\)+\(\frac{1}{2.3}\)+\(\frac{1}{3.4}\)+...+\(\frac{1}{49.50}\)
A=1-\(\frac{1}{2}\)+\(\frac{1}{2}\)-\(\frac{1}{3}\)+ \(\frac{1}{3}\) - \(\frac{1}{4}\)+...+\(\frac{1}{49}\)-\(\frac{1}{50}\)
A=1-\(\frac{1}{50}\)
A=\(\frac{49}{50}\)
