1.

\(\left(\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+...........+\dfrac{1}{8.9.10}\right)x=\dfrac{23}{45}\)

\(\Leftrightarrow\left[\dfrac{1}{2}\left(\dfrac{2}{1.2.3}+\dfrac{2}{3.4.5}+............+\dfrac{2}{8.9.10}\right)\right]x=\dfrac{23}{45}\)

\(\Leftrightarrow\left[\dfrac{1}{2}\left(\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+........+\dfrac{1}{8.9}-\dfrac{1}{9.10}\right)\right]x=\dfrac{23}{45}\)

\(\Leftrightarrow\left[\dfrac{1}{2}\left(\dfrac{1}{1.2}-\dfrac{1}{8.9}\right)\right]x=\dfrac{23}{45}\)

\(\Leftrightarrow\left[\dfrac{1}{2}.\dfrac{22}{45}\right]x=\dfrac{23}{45}\)

\(\Leftrightarrow\dfrac{11}{45}.x=\dfrac{23}{45}\)

\(\Leftrightarrow x=\dfrac{23}{11}\)

Vậy \(x=\dfrac{23}{11}\) là giá trị cần tìm

2.

\(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+.........+\dfrac{1}{x\left(x+1\right):2}=\dfrac{1998}{2000}\)

\(\Leftrightarrow\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{20}+...............+\dfrac{2}{x\left(x+1\right)}=\dfrac{1998}{2000}\)

\(\Leftrightarrow\dfrac{2}{2.3}+\dfrac{2}{3.4}+\dfrac{2}{4.5}+...........+\dfrac{2}{x\left(x+1\right)}=\dfrac{1998}{2000}\)

\(\Leftrightarrow2\left(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{5.6}+.........+\dfrac{1}{x\left(x+1\right)}\right)=\dfrac{1998}{2000}\)

\(\Leftrightarrow2\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+.........+\dfrac{1}{x}-\dfrac{1}{x+1}\right)=\dfrac{1998}{2000}\)

\(\Leftrightarrow2\left(\dfrac{1}{2}-\dfrac{1}{x+1}\right)=\dfrac{1998}{2000}\)

\(\Leftrightarrow\dfrac{1}{2}-\dfrac{1}{x+1}=\dfrac{999}{2000}\)

\(\Leftrightarrow\dfrac{1}{x+1}=\dfrac{1}{2000}\)

\(\Leftrightarrow x+1=2000\)

\(\Leftrightarrow x=1999\)

Vậy \(x=1999\) là giá trị cần tìm

2-3+4-5.......+2008-2009+2010-2011

\(=\left(2-3\right)+\left(4-5\right)+......+\left(2008-2009\right)+\left(2010-2011\right)\)(có tất cả 1005 số hạng -1)

\(=-1.1005=-1005\)

Học tốt

bạn chưa giải thích rõ ràng

có đấy thì làm sao :)

Ta có : abcabc : abc 

= (abc000 + abc) : abc 

= (abc.1000 + abc) : abc 

= abc . 1001 : abc 

= 1001 (đpcm)

abcabc= abc.1000+abc

           = abc.(1000+1)

           = abc.1001

 suy ra abcabc:abc = 1001 k nha

1.0.13

2.0.55

3.1,27 ♫ (•‿•)

13% = 0,13

55% = 0,55

127% = 1,27

nhớ k mình nha !

10195945

1019594,5

                Trồng cây theo hình ngôi sao nhé

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                     *        

    *                                * 

cậu có nik face ko ?

-3.-4.-5=-60

k mk nhé

20,7 + 1,47 : 7 - 0,23 x 5

= 20,7 + 0,21 - 1,15

= 20,91 - 1,15 

= 19,76

=20,7+0,21-1,15

=20,91-1,15

=19,76