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=>2A=4/2*6+4/6*10+4/10*14+...+4/42*46

=>2A=1/2-1/6+1/6-1/10+...+1/42-1/46=1/2-1/46=22/46

=>A=11/46

14 tháng 7 2023

\(A=\dfrac{1}{6}+\dfrac{1}{30}+\dfrac{1}{70}+\dfrac{1}{126}+...+\dfrac{1}{966}\)

\(\Rightarrow\dfrac{4}{2}A=\dfrac{4}{2}\cdot\left(\dfrac{1}{6}+\dfrac{1}{30}+\dfrac{1}{70}+...+\dfrac{1}{966}\right)\)

\(\Rightarrow2A=\dfrac{4}{2\times6}+\dfrac{4}{6\times10}+\dfrac{4}{10\times14}+\dfrac{4}{14\times18}+...+\dfrac{4}{42\times46}\)

\(\Rightarrow2A=\dfrac{1}{2}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{18}+...+\dfrac{1}{42}-\dfrac{1}{46}\)

\(\Rightarrow2A=\dfrac{1}{2}-\dfrac{1}{46}\)

\(\Rightarrow2A=\dfrac{11}{23}\)

\(\Rightarrow A=\dfrac{11}{23}:2\)

\(\Rightarrow A=\dfrac{11}{46}\)

28 tháng 1 2018

1) \(1+\frac{1}{3}+1\frac{91}{27}+\frac{1}{81}\)

\(=1+\frac{1}{3}+4+\frac{10}{27}+\frac{1}{81}\)

\(=\left(1+4\right)+\left(\frac{1}{3}+\frac{10}{27}+\frac{1}{81}\right)\)

\(=5+\frac{58}{81}=5\frac{58}{81}\)

2) \(\frac{1}{78}+\frac{1}{91}+\frac{1}{105}+\frac{1}{120}+\frac{1}{136}\)

\(=\frac{1}{6\times13}+\frac{1}{13\times7}+\frac{1}{7\times15}+\frac{1}{15\times8}+\frac{1}{8\times17}\)

\(=\frac{1}{6}-\frac{1}{13}+\frac{1}{13}-\frac{1}{7}+\frac{1}{7}-\frac{1}{15}+\frac{1}{15}-\frac{1}{8}+\frac{1}{8}-\frac{1}{17}\)

(gạch bỏ các số giống nhau)

\(=\frac{1}{6}-\frac{1}{17}=\frac{11}{102}\)

3)  \(\frac{1}{6}+\frac{1}{30}+\frac{1}{70}+\frac{1}{126}\)

\(=\frac{1}{2\times3}+\frac{1}{3\times10}+\frac{1}{10\times7}+\frac{1}{7\times18}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{10}+\frac{1}{10}-\frac{1}{7}+\frac{1}{7}-\frac{1}{18}\)

\(=\frac{1}{2}-\frac{1}{18}=\frac{4}{9}\)

chúc bn học tốt!!

28 tháng 1 2018

công chúa ôri ơi mk viết nhầm đề bài 1 

đề bài là 1+1/3+1/9+1/27+1/81

bạn trả lời giúp mk với mk cần gấp lắm

cảm ơn

a) 123,45 x 678 - 246,9 x 338 - 246

= 83699,1 - 83452,2 - 246

= 246,9 - 246

= 0,9

b, \(\frac{1}{6}+\frac{1}{11}+\frac{1}{70}+\frac{1}{126}+\frac{1}{198}+\frac{1}{286}\)

Bạn tính ra máy tính bỏ túi

23 tháng 8 2017

a) 0,9

b) 1237/4290

23 tháng 8 2017

lam rõ nha các bn

2 tháng 4 2021

b)575- [(-6)x+70]=445

-6x+70=575-445=130

-6x=130-70=60

x= 60:(-6)

x=-10

Vậy x=-10

c)

315+(125-x)=435

125-x= 435-315= 120

x=125-120

x=5

Vậy x= 5

26 tháng 8 2023

\(A=\dfrac{2}{1x3}+\dfrac{2}{3x5}+\dfrac{2}{5x7}+...+\dfrac{2}{21x23}\)

\(A=2x\left(\dfrac{1}{1x3}+\dfrac{1}{3x5}+\dfrac{1}{5x7}+...+\dfrac{1}{21x23}\right)\)

\(A=2x\dfrac{1}{2}x\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{21}-\dfrac{1}{23}\right)\)

\(A=1-\dfrac{1}{23}\)

\(A=\dfrac{22}{23}\)

26 tháng 8 2023

\(B=\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}\)

\(B=\dfrac{1}{2x3}+\dfrac{1}{3x4}+\dfrac{1}{4x5}+\dfrac{1}{5x6}+\dfrac{1}{6x7}+\dfrac{1}{7x8}+\dfrac{1}{8x9}+\dfrac{1}{9x10}\)

\(B=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\)

\(B=\dfrac{1}{2}-\dfrac{1}{10}\)

\(B=\dfrac{5}{10}-\dfrac{1}{10}\)

\(B=\dfrac{4}{10}\)

\(B=\dfrac{2}{5}\)

10 tháng 6 2019

a) 78 x 37 + 39 x 126

=  39 x 2 x 37 + 39 x 126

=  39 x 74 + 39 x 126

=   39 x ( 74 + 126 )

=  39 x 200

= 7800.

Học tốt.

10 tháng 6 2019

b) \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{72}\)

\(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{8\times9}\)

\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{8}-\frac{1}{9}\)

\(1-\frac{1}{9}\)

\(\frac{8}{9}\)

27 tháng 7

a; \(\dfrac{1}{4}\) + \(\dfrac{2}{5}\) + \(\dfrac{6}{8}\) + \(\dfrac{9}{15}\) + \(\dfrac{8}{1}\)

= (\(\dfrac{1}{4}\) + \(\dfrac{6}{8}\)) + (\(\dfrac{2}{5}\) + \(\dfrac{9}{15}\)) + \(\dfrac{8}{1}\)

= (\(\dfrac{1}{4}\) + \(\dfrac{3}{4}\)) + (\(\dfrac{2}{5}\) + \(\dfrac{3}{5}\)) + 8

=  1 + 1 + 8

=  2 + 8

= 10

27 tháng 7

b; \(\dfrac{1}{2}\) + \(\dfrac{2}{4}\) + \(\dfrac{3}{6}\) + \(\dfrac{4}{8}\) + \(\dfrac{5}{10}\) + \(\dfrac{6}{12}\) + \(\dfrac{7}{14}\) + \(\dfrac{8}{16}\) + \(\dfrac{10}{20}\)

=  \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) x (\(\dfrac{2}{2}\) + \(\dfrac{3}{3}\) + \(\dfrac{4}{4}\) + \(\dfrac{5}{5}\)\(\dfrac{6}{6}+\dfrac{7}{7}+\dfrac{8}{8}\) + \(\dfrac{10}{10}\))

\(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) x (1 + 1 +1 + 1+ 1+ 1+ 1 +1)

\(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) x 1 x 8

\(\dfrac{1}{2}\) + \(\)\(\dfrac{1}{2}\) x 8

\(\dfrac{1}{2}\) + 4

\(\dfrac{9}{2}\) 

 

21 tháng 9

a; \(\dfrac{1}{4}\) + \(\dfrac{2}{5}\) + \(\dfrac{6}{8}\) + \(\dfrac{9}{15}\) + \(\dfrac{8}{1}\)

  = (\(\dfrac{1}{4}\) + \(\dfrac{6}{8}\)) + (\(\dfrac{2}{5}\) + \(\dfrac{9}{15}\)) + 8

= (\(\dfrac{1}{4}\) + \(\dfrac{3}{4}\)) + (\(\dfrac{2}{5}\) + \(\dfrac{3}{5}\)) + 8

= 1 + 1 + 8

= 2 + 8

= 10

21 tháng 9

b; \(\dfrac{1}{2}\) + \(\dfrac{2}{4}\) + \(\dfrac{3}{6}\) + \(\dfrac{4}{8}\) + \(\dfrac{5}{10}\) + \(\dfrac{6}{12}\) + \(\dfrac{7}{14}\) + \(\dfrac{8}{16}\) + \(\dfrac{9}{18}\) + \(\dfrac{10}{20}\)

\(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\)

\(\dfrac{1}{2}\) x 10

= 5