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\(A=\frac{9}{1.2}+\frac{9}{2.3}+\frac{9}{3.4}+...+\frac{9}{2019.2020}\)

\(=9\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2019.2020}\right)\)

\(=9\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2019}-\frac{1}{2020}\right)\)

\(=9\left(1-\frac{1}{2020}\right)\)

\(=9.\frac{2019}{2020}\)

\(=\frac{18171}{2020}\)

13 tháng 3 2020

\(A=\frac{9}{1.2}+\frac{9}{2.3}+\frac{9}{3.4}+...+\frac{9}{2019.2020}\)

\(A=9.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2019.2020}\right)\)

\(A=9\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2019}-\frac{1}{2020}\right)\)

\(A=9\left(1-\frac{1}{2020}\right)=\frac{9.2019}{2020}=\frac{18171}{2020}\)

...

\(A=9\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{98\cdot99}\right)\)

\(=9\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{98}-\dfrac{1}{99}\right)\)

\(=9\cdot\dfrac{98}{99}=\dfrac{98}{11}\)

4 tháng 5 2016

A = 9/1.2 + 9/2.3 + 9/3.4 +...+ 9/98.99 + 9/99.100

   = 9. (1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/98 - 1/99 + 1/99 - 1/100)

   = 9. (1 - 1/100)

   = 9 . 99/100

   = 891/100

27 tháng 4 2016

\(A=9\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\right)\)

\(A=9\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\right)\)

\(A=9\left(1-\frac{1}{100}\right)\)

\(A=9\times\frac{99}{100}\)

\(A=\frac{891}{100}\) hoặc =8,91

27 tháng 4 2016

A=9/1.2+9/2.3+9/3.4+...+9/98.99+9/99.100

A=9.(1/1.2+1/2.3+1/3.4+...+1/98.99+1/99.100)

A=9.(1/1-1/2+1/2-1/3+1/3-1/4+...+1/98-1/99+1/99-1/100)

A=9.(1/1-1/100)

A=9.99/100

A=891/100

A=8+91/100 ( viết dưới dạng hỗn số )

Vậy A=8+91/100

Nkớ k cho mink đó nha !!!

A=9/1.2+ 9/2.3+ 9/3.4+ .... +9/98.99 + 9/99/100

  =9(1- 1/2 + 1/2 -1/3+...+1/99 -1/100)

  =9.(1- 1/100)

  =9.99/100

  =891/100

2 tháng 5 2019

A=9/1.2+9/2.3+...+9/99.100

A/9=1/1.2+1/2.3+....+1/99.100

A/9=1-1/2+1/2-1/3+....+1/99-1/100

A/9=1+(-1/2+1/2)+(-1/3+1/3)+....+(-1/99+1/99)-1/100

A/9=1-1/100

A/9=99/100

A=99/100.9=891/100

     Vậy A=891/100

 mik ko biết đúng hay sai mn góp ý giúp mik nha

13 tháng 3 2022

\(A=9\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{99}-\dfrac{1}{100}\right)=9\left(1-\dfrac{1}{100}\right)=\dfrac{891}{100}\)

7 tháng 2 2023

\(\dfrac{-1}{9}.\dfrac{-3}{5}+\dfrac{5}{-6}.\dfrac{-3}{5}-\dfrac{7}{2}.\dfrac{3}{5}\)

\(=\dfrac{3}{5}.\left(\dfrac{1}{9}+\dfrac{5}{6}-\dfrac{7}{2}\right)\)

\(=\dfrac{3}{5}.\left(\dfrac{2}{18}+\dfrac{15}{18}-\dfrac{63}{18}\right)\)

\(=\dfrac{3}{5}.\left(-\dfrac{23}{9}\right)\)

\(=-\dfrac{69}{45}\)

7 tháng 2 2023

`6/7 . 8/13 +6/7 . 9/13+3/13 . 6/7`

`=6/7 . (8/13+9/13+3/13)`

`=6/7 . 20/13`

`=120/91`

7 tháng 2 2023

\(\dfrac{6}{7}.\dfrac{8}{13}+\dfrac{6}{7}.\dfrac{9}{13}+\dfrac{3}{13}.\dfrac{6}{7}\)

\(=\dfrac{6}{7}.\left(\dfrac{8}{13}+\dfrac{9}{13}+\dfrac{3}{13}\right)\)

\(=\dfrac{6}{7}.\left(\dfrac{8+9+3}{13}\right)\)

\(=\dfrac{6}{7}.\dfrac{20}{13}\)

\(=\dfrac{6.20}{7.13}\)

\(=\dfrac{120}{91}\)

27 tháng 4 2016

\(A=\frac{9}{1.2}+\frac{9}{2.3}+\frac{9}{3.4}+...+\frac{9}{98.99}+\frac{9}{99.100}\)

\(A=\frac{1}{9}.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{98.99}+\frac{1}{99.100}\right)\)

\(A=\frac{1}{9}.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\right)\)

\(A=\frac{1}{9}.\left(1-\frac{1}{100}\right)\)

\(A=\frac{1}{9}.\frac{99}{100}\)

\(A=\frac{11}{100}\)

27 tháng 4 2016

A = 9/1.2 + 9/2.3 + 9/3.4 +...+ 9/98.99 + 9/99.100

   = 9. (1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/98 - 1/99 + 1/99 - 1/100)

   = 9. (1 - 1/100)

   = 9 . 99/100

   = 891/100