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29 tháng 3 2017

\(G=\dfrac{3}{2^2}.\dfrac{8}{3^2}.\dfrac{15}{4^2}....\dfrac{899}{30^2}\)

\(G=\dfrac{1.3}{2.2}.\dfrac{2.4}{3.3}.\dfrac{3.5}{4.4}....\dfrac{29.31}{30.30}\)

\(G=\dfrac{1.3.2.4.3.5....29.31}{2.2.3.3.4.4....30.30}\)

\(G=\dfrac{1.2.3....29}{2.3.4....30}.\dfrac{3.4.5....31}{2.3.4....30}\)

G=\(\dfrac{1}{30}.\dfrac{31}{2}=\dfrac{31}{60}\)

29 tháng 3 2017

\(G=\dfrac{3}{2^2}.\dfrac{8}{3^2}.\dfrac{15}{4^2}........................\dfrac{899}{30^2}\)

\(G=\dfrac{1.3}{2.2}.\dfrac{2.4}{3.3}.\dfrac{3.5}{4.4}................\dfrac{29.31}{30.30}\)

\(G=\dfrac{2.3.4...........30}{2.3.4.............30}.\dfrac{1.3.4..............31}{2.3.4.............30}\)

\(G=\dfrac{31}{2}\)

26 tháng 2 2021

\(\dfrac{3}{2^2}.\dfrac{8}{3^2}.\dfrac{15}{4^2}.....\dfrac{899}{30^2}\)

\(\dfrac{1.3}{2.2}.\dfrac{2.4}{3.3}.\dfrac{3.5}{4.4}.....\dfrac{29.31}{30.30}\) 

\(\dfrac{1.3.2.4.3.5.....29.31}{2.2.3.3.4.4.....30.30}\)

=\(\dfrac{\left(1.2.3.....29\right).\left(3.4.5......31\right)}{\left(2.3.4......30\right).\left(2.3.4.....30\right)}\) 

\(\dfrac{1.31}{2.30}\) 

\(\dfrac{31}{60}\)

Ta có: \(\dfrac{3}{2^2}\cdot\dfrac{8}{3^2}\cdot\dfrac{15}{4^2}\cdot...\cdot\dfrac{899}{30^2}\)

\(=\dfrac{1\cdot3}{2\cdot2}\cdot\dfrac{2\cdot2^2}{3\cdot3}\cdot\dfrac{3\cdot5}{4\cdot4}\cdot...\cdot\dfrac{29\cdot31}{30\cdot30}\)

\(=\dfrac{\left(1\cdot2\cdot3\cdot...\cdot29\right)\cdot\left(3\cdot4\cdot5\cdot...\cdot31\right)}{\left(2\cdot3\cdot4\cdot...\cdot30\right)\left(2\cdot3\cdot4\cdot...\cdot30\right)}\)

\(=\dfrac{1\cdot31}{2\cdot30}=\dfrac{31}{60}\)

4 tháng 7 2017

\(A=\dfrac{3}{2^2}.\dfrac{8}{3^2}.\dfrac{15}{4^2}.....\dfrac{899}{30^2}\)

\(A=\dfrac{1.3}{2.2}.\dfrac{2.4}{3.3}.\dfrac{3.5}{4.4}.....\dfrac{29.31}{30.30}\)

\(A=\dfrac{1.3.2.4.3.5.....29.31}{2.2.3.3.4.4.....30.30}\)

\(A=\dfrac{1.2.3.....29}{2.3.4....30}.\dfrac{3.4.5.....31}{2.3.4.....30}\)

\(A=\dfrac{1}{30}.\dfrac{31}{2}=\dfrac{31}{60}\)

\(B=\dfrac{8}{9}.\dfrac{15}{16}.\dfrac{24}{25}.....\dfrac{2499}{2500}\)

\(B=\dfrac{2.4}{3.3}.\dfrac{3.5}{4.4}.\dfrac{4.6}{5.5}.....\dfrac{49.51}{50.50}\)

\(B=\dfrac{2.4.3.5.4.6.....49.51}{3.3.4.4.5.5....50.50}\)

\(B=\dfrac{2.3.4......49}{3.4.5....50}.\dfrac{4.5.6.....51}{3.4.5....50}\)

\(B=\dfrac{2}{50}.\dfrac{51}{3}=\dfrac{17}{25}\)

4 tháng 7 2017

Giải:

\(A=\dfrac{3}{2^2}.\dfrac{8}{3^2}.\dfrac{15}{4^2}.....\dfrac{899}{30^2}.\)

\(A=\dfrac{1.3}{2^2}.\dfrac{2.4}{3^2}.\dfrac{3.5}{4^2}.....\dfrac{29.31}{30^2}.\)

\(A=\dfrac{1.2.3.....29}{2.3.4.....30}.\dfrac{2.3.4.....31}{2.3.4.....30}.\)

\(A=\dfrac{1}{30}.31=\dfrac{30}{31}.\)

Vậy \(A=\dfrac{30}{31}.\)

22 tháng 4 2021

Tìm y:

-y:1/2-5/2=4+1/2

-y:1/2 = 4+1/2+5/2

-y:1/2 = 7

-y = 7.2

y = -14

Vậy y = -14

6 tháng 2 2023

`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`

6 tháng 2 2023

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)\(-\dfrac{1}{2}+\dfrac{3}{21}+-\dfrac{2}{6}+-\dfrac{5}{30}\)
\(=-\dfrac{1}{2}+\dfrac{1}{7}+-\dfrac{1}{3}+-\dfrac{1}{6}\)
\(=\left(-\dfrac{1}{2}+-\dfrac{1}{3}+-\dfrac{1}{6}\right)+\dfrac{1}{7}\)
\(=-\dfrac{3+2+1}{6}+\dfrac{1}{7}\)
\(=\dfrac{1}{7}-1\)
\(=\dfrac{1}{7}-\dfrac{7}{7}=-\dfrac{6}{7}\)

20 tháng 4 2022

c) \(\dfrac{11}{10}-\dfrac{-7}{24}=\dfrac{11}{10}+\dfrac{7}{24}=\dfrac{167}{120}\)

e) \(\dfrac{-8}{3}\cdot\dfrac{15}{7}=\dfrac{-120}{21}=\dfrac{-40}{7}\)

f) \(\dfrac{-2}{5}\cdot4\dfrac{1}{2}=\dfrac{-2}{5}\cdot\dfrac{9}{2}=-\dfrac{9}{5}\)

g) \(\dfrac{5}{3}:\dfrac{5}{-3}=\dfrac{5}{3}:\dfrac{-5}{3}=\dfrac{5}{3}\cdot\dfrac{-3}{5}=-1\)

h) \(\dfrac{5}{4}:\left(-9\right)=\dfrac{5}{4}:\dfrac{-9}{1}=\dfrac{5}{4}\cdot\dfrac{-1}{9}=-\dfrac{5}{36}\)

22 tháng 2 2023

`a, -21/15 . (-10)/14 = 210/210=1`

`b, (-2/3)^2= 4/9`

`c, (-3)/4 . (-4)/5 . 16/9= 192/180=16/15`

`d, (-8)/3 . 5/6= -40/18=-20/9`

`e, 16/30 . 5/12= 8/15 . 5/12=40/180=2/9`

`f, 13/30 . (-1)/5= -13/150`

`g, 2/21 . 3/28= 6/588= 1/98`

`h, (-3/4)^3= -27/64`

27 tháng 2 2022

Đề bài là:Tính các giá trị biểu thức sau ạ

a: \(=\left(9-\dfrac{13}{18}\right):\dfrac{325}{27}-\dfrac{17}{8}:\dfrac{51}{40}\)

\(=\dfrac{149}{18}\cdot\dfrac{27}{325}-\dfrac{17}{8}\cdot\dfrac{40}{51}\)

\(=\dfrac{447}{650}-\dfrac{5}{3}=-\dfrac{1909}{1950}\)

b: \(=\dfrac{48}{64}+\left(\dfrac{4}{5}-2-\dfrac{4}{15}\right):\dfrac{11}{3}\)

\(=\dfrac{3}{4}+\dfrac{-22}{15}\cdot\dfrac{3}{11}=\dfrac{3}{4}-\dfrac{2}{5}=\dfrac{15-8}{20}=\dfrac{7}{20}\)

18 tháng 6 2018

\(A=\dfrac{3}{4}\cdot\dfrac{8}{9}\cdot\dfrac{15}{16}\cdot...\cdot\dfrac{899}{900}\\ =\dfrac{1\cdot3}{2\cdot2}\cdot\dfrac{2\cdot4}{3\cdot3}\cdot\dfrac{3\cdot5}{4\cdot4}\cdot...\cdot\dfrac{29\cdot31}{30\cdot30}\\ =\dfrac{1\cdot2\cdot3\cdot...\cdot29}{2\cdot3\cdot4\cdot...\cdot30}\cdot\dfrac{3\cdot4\cdot5\cdot...\cdot31}{2\cdot3\cdot4\cdot...\cdot30}\\ =\dfrac{1}{30}\cdot\dfrac{31}{2}\\ =\dfrac{31}{60}\)

Vậy ...

21 tháng 3 2022

\(a,\dfrac{-8}{15}+\dfrac{13}{30}-\dfrac{5}{12}=\dfrac{-32}{60}+\dfrac{26}{60}-\dfrac{25}{60}=-\dfrac{31}{60}\\ b,\dfrac{3}{2}.\dfrac{7}{2}+\left(\dfrac{-5}{6}+\dfrac{1}{10}:\dfrac{11}{30}\right)=\dfrac{21}{4}+\left(\dfrac{-5}{6}+\dfrac{3}{11}\right)=\dfrac{21}{4}+\dfrac{-37}{66}=\dfrac{619}{132}\)

\(c,\dfrac{-20}{21}.\dfrac{22}{35}+\dfrac{-20}{21}.\dfrac{13}{35}+\dfrac{-22}{21}=\dfrac{-20}{21}\left(\dfrac{22}{35}+\dfrac{13}{35}\right)+\dfrac{-22}{21}=\dfrac{-20}{21}.1+\dfrac{-22}{21}=\dfrac{-20}{21}+\dfrac{-22}{21}=\dfrac{-42}{21}=-2\)