khó à nha

tôi mới lên lớp 5 thôi nên  ko có biết !!!

sorry nha

   \(\dfrac{3}{2.6}\) + \(\dfrac{3}{6.10}\) + \(\dfrac{3}{10.14}\)

=  \(\dfrac{3}{4}\).(\(\dfrac{4}{2.6}\) + \(\dfrac{4}{6.10}\) + \(\dfrac{4}{10.14}\))

= \(\dfrac{3}{4}\).(\(\dfrac{1}{2}-\dfrac{1}{6}\) + \(\dfrac{1}{6}\) - \(\dfrac{1}{10}\) + \(\dfrac{1}{10}\) - \(\dfrac{1}{14}\))

= \(\dfrac{3}{4}\).(\(\dfrac{1}{2}\) - \(\dfrac{1}{14}\))

= \(\dfrac{3}{4}\). \(\dfrac{3}{7}\)

= \(\dfrac{9}{28}\)

B = \(\dfrac{4}{1.3.5}\) + \(\dfrac{4}{3.5.7}\) + \(\dfrac{4}{5.7.9}\)

B = \(\dfrac{1}{1.3}\) - \(\dfrac{1}{3.5}\) + \(\dfrac{1}{3.5}\) - \(\dfrac{1}{5.7}\) + \(\dfrac{1}{5.7}\) - \(\dfrac{1}{7.9}\)

B = \(\dfrac{1}{1.3}\) - \(\dfrac{1}{7.9}\)

B = \(\dfrac{1}{3}\) - \(\dfrac{1}{63}\)

B =  \(\dfrac{20}{63}\)

C = \(\dfrac{5}{2.4.6}\) + \(\dfrac{5}{4.6.8}\) + \(\dfrac{5}{6.8.10}\)

C = \(\dfrac{5}{4}\).(\(\dfrac{4}{2.4.6}\) + \(\dfrac{4}{4.6.8}\) + \(\dfrac{4}{6.8.10}\))

C = \(\dfrac{5}{4}\).(\(\dfrac{1}{2.4}\) - \(\dfrac{1}{4.6}\) + \(\dfrac{1}{4.6}\) - \(\dfrac{1}{6.8}\) + \(\dfrac{1}{6.8}\) - \(\dfrac{1}{8.10}\))

C = \(\dfrac{5}{4}\).(\(\dfrac{1}{2.4}\) - \(\dfrac{1}{8.10}\))

C = \(\dfrac{5}{4}\).( \(\dfrac{1}{8}\) - \(\dfrac{1}{80}\))

C = \(\dfrac{5}{4}\). \(\dfrac{9}{80}\)

C = \(\dfrac{9}{64}\)

\(A=\dfrac{2.6.10+6.10.14+10.14.18+..+194.198.202}{1.3.5+3.5.7+5.7.9+..+97.99.101}\)

\(=\dfrac{2^3.1.3.5+2^3.3.5.7+2^3.5.7.9+...+2^3.97.99.101}{1.3.5+3.5.7+7.9.11+...+97.99.101}\)

\(=\dfrac{2^3.\left(1.3.5+3.5.7+7.9.11+...+97.99.101\right)}{1.3.5+3.5.7+5.7.9+...+97.99.101}=2^3=8\)

ta có tử =2.(1.3.5)+2.(3.5.7)+2.(5.7.9)+....+2.(97.99.101)

             =2.(1.3.5+3.5.7+5.7.9+....+97.99.101)

mà mẫu =1.3.5+3.5.7+5.7.9+...+97.99.101

suy ra A=2