Question

[Ha Nguyen]

giúp nhanh !!!!

Answer 1

[Nguyễn Thị Thương Hoài]

Bài 15:

\(\dfrac{1}{1\times3\times7}\)+\(\dfrac{1}{3\times7\times9}\)+\(\dfrac{1}{7\times9\times13}\)+\(\dfrac{1}{9\times13\times15}\)+\(\dfrac{1}{13\times15\times19}\)

= \(\dfrac{1}{6}\).(\(\dfrac{6}{1\times3\times7}\)+\(\dfrac{6}{3\times7\times9}\)+\(\dfrac{6}{7\times9\times13}\)+\(\dfrac{6}{9\times13\times15}\)+\(\dfrac{6}{13\times15\times19}\))

=\(\dfrac{1}{6}\).(\(\dfrac{1}{1.3}\)-\(\dfrac{1}{3.7}\)+\(\dfrac{1}{3.7}\)-\(\dfrac{1}{7.9}\)+\(\dfrac{1}{7.9}\)-\(\dfrac{1}{9.13}\)+\(\dfrac{1}{9.13}\)-\(\dfrac{1}{13.15}\)+\(\dfrac{1}{13.15}\)-\(\dfrac{1}{15.19}\))

= \(\dfrac{1}{6}\).(\(\dfrac{1}{1.3}\) - \(\dfrac{1}{15.19}\))

= \(\dfrac{1}{6}\).(\(\dfrac{1}{3}\)-\(\dfrac{1}{285}\))

= \(\dfrac{1}{6}\).\(\dfrac{94}{285}\)

=\(\dfrac{47}{855}\)

Dấu chấm là dấu nhân em nhá

Answer 2

[Nguyễn Thị Thương Hoài]

Bài 16:

2 - (\(\dfrac{1}{1\times5}\)+ \(\dfrac{1}{5\times9}\)+ \(\dfrac{1}{9\times13}\)+ \(\dfrac{1}{13\times17}\)+ \(\dfrac{1}{17\times21}\))

= 2 - \(\dfrac{1}{4}\) \(\times\)( \(\dfrac{4}{1\times5}\)+\(\dfrac{4}{5\times9}\)+\(\dfrac{4}{9\times13}\)+\(\dfrac{4}{13\times17}\)+\(\dfrac{1}{17\times21}\))

= 2 - \(\dfrac{1}{4}\)\(\times\)(\(\dfrac{1}{1}\)-\(\dfrac{1}{5}\)+\(\dfrac{1}{5}\)-\(\dfrac{1}{9}\)+\(\dfrac{1}{9}\)-\(\dfrac{1}{13}\)+\(\dfrac{1}{13}-\dfrac{1}{17}\)+\(\dfrac{1}{17}-\dfrac{1}{21}\))

= 2 - \(\dfrac{1}{4}\)\(\times\)(1- \(\dfrac{1}{21}\))

= 2 - \(\dfrac{1}{4}\)\(\times\)\(\dfrac{20}{21}\)

= 2 - \(\dfrac{5}{21}\)

= \(\dfrac{37}{21}\)