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C1:5/7×13/21+2/7×13/21
=65/147+26/147
=91/147
C2=5/7×13/21+2/7×13/21
=(5/7+2/7)×13/21
=7/7×13/21
=91/147
5/7×13/21+2/7+13/21
=(5/7+2/7)×13/21
=1×13/21
=13/21
A = \(\dfrac{2}{1\times3}\) + \(\dfrac{2}{3\times5}\) + \(\dfrac{2}{5\times7}\) + \(\dfrac{2}{7\times9}\)
A = \(\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}\) + \(\dfrac{1}{7}-\dfrac{1}{9}\)
A = \(\dfrac{1}{1}-\dfrac{1}{9}\)
A = \(\dfrac{8}{9}\)
B = \(\dfrac{1}{3}+\dfrac{1}{15}\) + \(\dfrac{1}{35}+\) \(\dfrac{1}{63}\) + ... + \(\dfrac{1}{195}\)
B = \(\dfrac{1}{1\times3}\) + \(\dfrac{1}{3\times5}\) + \(\dfrac{1}{5\times7}\) + ...+ \(\dfrac{1}{13\times15}\)
B = \(\dfrac{1}{2}\) x (\(\dfrac{2}{1\times3}\) + \(\dfrac{2}{3\times5}\) + \(\dfrac{2}{5\times7}\) + ..+ \(\dfrac{1}{13}\) - \(\dfrac{1}{15}\))
B = \(\dfrac{1}{2}\) x (\(\dfrac{1}{1}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}-\dfrac{1}{5}\) + ...+\(\dfrac{1}{13}-\dfrac{1}{15}\))
B = \(\dfrac{1}{2}\) x (\(\dfrac{1}{1}-\dfrac{1}{15}\))
B = \(\dfrac{1}{2}\) x \(\dfrac{14}{15}\)
B = \(\dfrac{7}{15}\)
\(\dfrac{7}{5}:x=\dfrac{25}{37}.\dfrac{13}{21}+\dfrac{2}{7}.\dfrac{13}{21}\)
\(\dfrac{7}{5}:x=\dfrac{13}{21}.\left(\dfrac{25}{37}+\dfrac{2}{7}\right)\)
\(\dfrac{7}{5}:x=\dfrac{1079}{1813}\)
\(x=\dfrac{12691}{5395}\)
a=\(1\times3+\dfrac{2}{3}\times7+\dfrac{3}{7}\times13+\dfrac{4}{13}\times21+\dfrac{5}{12}\times21\)
=3+\(\dfrac{14}{3}\)+\(\dfrac{39}{7}\)+\(\dfrac{84}{13}\)+5=8+\(\dfrac{215}{21}\)+\(\dfrac{84}{13}\)=\(\dfrac{4559}{273}\)+8=\(\dfrac{6743}{273}\)