Question

tính nhanh 

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

\(\frac{4}{1.3.5}+\frac{4}{3.5.7}+\frac{4}{5.7.9}\)

\(\frac{5}{2.4.6}+\frac{5}{4.6.8}+\frac{5}{6.8.10}\)

Answer 1

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

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

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

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

= \(\dfrac{3}{4}\). \(\dfrac{3}{7}\)

= \(\dfrac{9}{28}\)

Answer 2

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 =  \(\dfrac{20}{63}\)

Answer 3

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 = \(\dfrac{9}{64}\)