A = \(-\frac{513}{100}:\left(\frac{145}{4.7}-\frac{17}{9}.\frac{5}{4}+\frac{79}{7.9}\right)=-\frac{513}{100}:\frac{145.9-17.5.7+79.4}{4.7.9}=-\frac{513}{100}:\frac{57}{14}\)

A = \(-\frac{513}{100}.\frac{14}{57}=\frac{-63}{50}\)

Đặt A=\(\frac{13}{21}-\frac{15}{28}+\frac{17}{36}-...+\frac{197}{4851}-\frac{199}{4950}\)

\(\frac{A}{2}=\frac{13}{42}-\frac{15}{56}+\frac{17}{72}-...+\frac{197}{9702}-\frac{199}{4950}\)

\(=\frac{6+7}{6.7}-\frac{7+8}{7.8}+\frac{8+9}{8.9}-...+\frac{98+99}{98.99}-\frac{99+100}{99.100}\)

\(=\frac{1}{7}+\frac{1}{6}-\frac{1}{8}-\frac{1}{7}+\frac{1}{9}+\frac{1}{8}-...+\frac{1}{99}+\frac{1}{98}-\frac{1}{100}+\frac{1}{99}\)

\(=\frac{1}{6}-\frac{1}{100}=\frac{47}{300}\)

\(\Rightarrow A=\frac{47}{300}.2=\frac{47}{150}\)

\(\Rightarrow Q=\frac{85}{25}+\frac{9}{10}-\frac{11}{5}+\frac{47}{150}=\frac{181}{75}\)

Vậy Q=\(\frac{181}{75}\).

a) \(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}+\frac{1}{195}\)

\(=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}+\frac{1}{13.15}\)

\(=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}\right)\)

\(=\frac{1}{2}.\left(1-\frac{1}{15}\right)\)

\(=\frac{1}{2}.\frac{14}{15}\)

\(=\frac{14}{30}=\frac{7}{15}\)

a)

\(=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}+\frac{1}{13.15}\)

\(=2\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}\right)\)

\(=2\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\right)\)

\(=2\left(1-\frac{1}{15}\right)\)

\(=2.\frac{14}{15}\)

\(=\frac{28}{15}\)

b)

\(=1+\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+\frac{2}{90}+\frac{2}{110}+\frac{2}{132}\)

\(=1+\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}+\frac{2}{7.8}+\frac{2}{8.9}+\frac{2}{9.10}+\frac{2}{10.11}+\frac{2}{11.12}\)

                                                                                         \(...\)

câu a mình nhầm phải là ½.(…)

\(\left(\frac{1}{3}+\frac{12}{67}+\frac{13}{41}\right)-\left(\frac{79}{67}-\frac{28}{41}\right)\)

\(=\frac{1}{3}+\frac{12}{67}+\frac{13}{41}-\frac{79}{67}-\frac{28}{41}\)

\(=\left(\frac{12}{67}-\frac{79}{67}\right)+\left(\frac{13}{41}+\frac{28}{41}\right)+\frac{1}{3}\)

\(=\left(-1\right)+1+\frac{1}{3}\)

\(=0+\frac{1}{3}\)

\(=\frac{1}{3}\)

=1/3+12/67+13/41-79/67+28/41

=1/3+(12/67-79/67)+(13/41+28/41)

=1/3+(-1)+1

=1/3+0

=1/3

hoang xuan ngan bạn tả lời sai rồi đó nhiên