\(\dfrac{2}{7x9}+\dfrac{2}{9x11}+.......+\dfrac{2}{19+21}\)
\(\dfrac{2}{1x3} + \dfrac{2}{3x5} + \dfrac{2}{5x7} + \dfrac{2}{7x9} + \dfrac{2}{9x11}\)
\(\dfrac{2}{1x3}+\dfrac{2}{3x5}+\dfrac{2}{5x7}+\dfrac{2}{7x9}+\dfrac{2}{9x11}\)
giúp mik với ạk
\(\dfrac{2}{1\times3}+\dfrac{2}{3\times5}+\dfrac{2}{5\times7}+\dfrac{2}{7\times9}+\dfrac{2}{9\times11}\)
\(=2\times\left(\dfrac{1}{1\times3}+\dfrac{1}{3\times5}+\dfrac{1}{5\times7}+\dfrac{1}{7\times9}+\dfrac{1}{9\times11}\right)\)
\(=2\times\dfrac{1}{2}\times\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}\right)\)
\(=1-\dfrac{1}{11}\)
\(=\dfrac{11}{11}-\dfrac{1}{11}\)
\(=\dfrac{10}{11}\)
\(\dfrac{2}{1\times3}+\dfrac{2}{3\times5}+\dfrac{2}{5\times7}+\dfrac{2}{7\times9}+\dfrac{2}{9\times11}\\ =1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}\\ =1-\dfrac{1}{11}\\ =\dfrac{10}{11}\)
\(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{9\cdot11}\)
\(=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{9}-\dfrac{2}{11}\)
\(=1-\dfrac{2}{11}\)
\(=\dfrac{9}{11}\)
3/ Tính hợp lí :
a/ P = \(\dfrac{-2}{7}\) + \(\dfrac{14}{29}\) + \(\dfrac{12}{33}\) + \(\dfrac{15}{29}\) + \(\dfrac{21}{33}\) + \(\dfrac{2}{7}\)
b/ \(\dfrac{2}{7}\) . \(\dfrac{5}{19}\) + \(\dfrac{2}{7}\) . \(\dfrac{14}{19}\) + \(\dfrac{21}{19}\) - \(\dfrac{2}{7}\) . \(\dfrac{1}{5}\)
a)P=\(\dfrac{-2}{7}+\dfrac{14}{29}+\dfrac{12}{33}+\dfrac{15}{29}+\dfrac{21}{33}+\dfrac{2}{7}\)
=\(\left(\dfrac{-2}{7}+\dfrac{2}{7}\right)+\left(\dfrac{14}{29}+\dfrac{15}{29}\right)+\left(\dfrac{12}{33}+\dfrac{21}{33}\right)\)
=0+1+1=2
b)\(\dfrac{2}{7}.\dfrac{5}{19}+\dfrac{2}{7}.\dfrac{14}{19}+\dfrac{21}{19}-\dfrac{2}{7}.\dfrac{1}{5}\)
=\(\dfrac{2}{7}.\left(\dfrac{5}{19}+\dfrac{14}{19}-\dfrac{1}{5}\right)+\dfrac{21}{19}\)
=\(\dfrac{2}{7}.\dfrac{4}{5}+\dfrac{21}{19}=\dfrac{887}{665}\)
bài 2: kết quả phép tính \(\dfrac{7}{19}\) x \(\dfrac{1}{3}\) + \(\dfrac{7}{19}\) x \(\dfrac{2}{3}\)=
a. \(\dfrac{14}{21}\)
b.\(\dfrac{21}{19}\)
c.\(\dfrac{14}{57}\)
d.\(\dfrac{7}{19}\)
\(1-\dfrac{2}{3x5}-\dfrac{2}{5x7}-\dfrac{2}{7x9}-...-\dfrac{2}{19x21}\)
\(=1-\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{19}-\dfrac{1}{21}\right)\)
\(=1-\dfrac{6}{21}=\dfrac{15}{21}=\dfrac{5}{7}\)
Tính bằng cách thuận tiện.
a) \(\dfrac{3}{5}\times\dfrac{17}{21}+\dfrac{2}{5}\times\dfrac{17}{21}\) b) \(\dfrac{11}{19}\times\dfrac{2}{7}+\dfrac{5}{7}\times\dfrac{11}{19}\)
a) \(\dfrac{3}{5}\times\dfrac{17}{21}+\dfrac{2}{5}\times\dfrac{17}{21}\)
\(=\dfrac{17}{21}\times\left(\dfrac{3}{5}+\dfrac{2}{5}\right)\)
\(=\dfrac{17}{21}\times1\)
\(=\dfrac{17}{21}\)
b) \(\dfrac{11}{19}\times\dfrac{2}{7}+\dfrac{5}{7}\times\dfrac{11}{19}\)
\(=\dfrac{11}{19}\times\left(\dfrac{2}{7}+\dfrac{5}{7}\right)\)
\(=\dfrac{11}{19}\times1\)
\(=\dfrac{11}{19}\)
a: =17/21(3/5+2/5)
=17/21*5/5
=17/21
b: =11/19(2/7+5/7)
=11/19*1
=11/19
Tính tổng sau:
\(\dfrac{2}{3X5}+\dfrac{2}{5X7}+\dfrac{2}{7X9}+...+\dfrac{2}{19X21}\)
`2/[3.5]+2/[5.7]+2/[7.9]+....+2/[19.21]`
`=1/3-1/5+1/5-1/7+1/7-1/9+....+1/19-1/21`
`=1/3-1/21`
`=6/21`
f\(\dfrac{-2}{17}+\dfrac{15}{23}+\dfrac{-15}{17}+\dfrac{4}{19}+\dfrac{8}{23}\)
g \(\dfrac{-1}{2}+\dfrac{3}{21}+\dfrac{-2}{6}+\dfrac{-5}{30}\)
f)\(-\dfrac{2}{17}+\dfrac{15}{23}+-\dfrac{15}{17}+\dfrac{4}{19}+\dfrac{8}{23}\)
\(=\left(-\dfrac{2}{17}+-\dfrac{15}{17}\right)+\left(\dfrac{15}{23}+\dfrac{8}{23}\right)+\dfrac{4}{19}\)
\(=-1+1+\dfrac{4}{19}\)
\(=0+\dfrac{4}{19}=\dfrac{4}{19}\)
g)\(-\dfrac{1}{2}+\dfrac{3}{21}+-\dfrac{2}{6}+-\dfrac{5}{30}\)
\(=-\dfrac{1}{2}+\dfrac{1}{7}+-\dfrac{1}{3}+-\dfrac{1}{6}\)
\(=\left(-\dfrac{1}{2}+-\dfrac{1}{3}+-\dfrac{1}{6}\right)+\dfrac{1}{7}\)
\(=-\dfrac{3+2+1}{6}+\dfrac{1}{7}\)
\(=\dfrac{1}{7}-1\)
\(=\dfrac{1}{7}-\dfrac{7}{7}=-\dfrac{6}{7}\)
`f)(-2)/17 + 15/23 + (-15)/17 + 4/19 + 8/23`
`= (-2/17+ -15/17)+(15/23+8/23)+4/19`
`= -1+1+4/19`
`= 0 +4/19`
`= 0`
`g)(-1)/2 + 3/21 + (-2)/6 + (-5)/30`
`= (-1)/2 + 1/7 + (-1)/3 + (-1)/6`
`= (-21)/42 + 6/42 + (-14)/42 + (-7)/42`
`=(-36)/42`
`=(-6)/7`
\(f,-\dfrac{2}{17}+\dfrac{15}{23}-\dfrac{15}{17}+\dfrac{4}{19}+\dfrac{8}{23}\)
\(=-\dfrac{2}{17}-\dfrac{15}{17}+\dfrac{15}{23}+\dfrac{8}{23}+\dfrac{4}{19}\)
\(=-1+1+\dfrac{4}{19}\)
\(=\dfrac{4}{19}\)
\(g,-\dfrac{1}{2}+\dfrac{3}{21}-\dfrac{2}{6}-\dfrac{5}{30}\)
\(=-\dfrac{5}{14}-\dfrac{1}{2}\)
\(=-\dfrac{5}{14}-\dfrac{7}{14}\)
\(=-\dfrac{6}{7}\)
a,\((\) 1\(-\) \(\dfrac{1}{3}\)\()\)x\((\)1\(-\)\(\dfrac{2}{5}\)\()\)x\((\)1\(-\)\(\dfrac{2}{7}\)\()\)x\((\)1\(-\)\(\dfrac{2}{9}\)\()\)
b,\(\dfrac{1}{1x3}\) + \(\dfrac{1}{3x5}\) + \(\dfrac{1}{5x7}\) + \(\dfrac{1}{7x9}\)
a) \(\left(1-\dfrac{1}{3}\right)\times\left(1-\dfrac{2}{5}\right)\times\left(1-\dfrac{2}{7}\right)\times\left(1-\dfrac{2}{9}\right)\)
\(=\left(\dfrac{3}{3}-\dfrac{1}{3}\right)\times\left(\dfrac{5}{5}-\dfrac{2}{5}\right)\times\left(\dfrac{7}{7}-\dfrac{2}{7}\right)\times\left(\dfrac{9}{9}-\dfrac{2}{9}\right)\)
\(=\dfrac{2}{3}\times\dfrac{3}{5}\times\dfrac{5}{7}\times\dfrac{7}{9}\)
\(=\dfrac{2\times3\times5\times7}{3\times5\times7\times9}\)
\(=\dfrac{2}{9}\)
b) \(\dfrac{1}{1\times3}+\dfrac{1}{3\times5}+\dfrac{1}{5\times7}+\dfrac{1}{7\times9}\)
\(=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}\)
\(=1-\dfrac{1}{9}\)
\(=\dfrac{9}{9}-\dfrac{1}{9}\)
\(=\dfrac{8}{9}\)