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\(\dfrac{1}{19}+\dfrac{9}{19\cdot29}+...+\dfrac{9}{1999\cdot2009}\)

\(=\dfrac{1}{19}+\dfrac{9}{10}\left(\dfrac{10}{19\cdot29}+...+\dfrac{10}{1999\cdot2009}\right)\)

\(=\dfrac{1}{19}+\dfrac{9}{10}\left(\dfrac{1}{19}-\dfrac{1}{2009}\right)\)

\(=\dfrac{1}{19}+\dfrac{1791}{38171}=\dfrac{200}{2009}\)

25 tháng 1 2017

\(A=\frac{1}{19}+\frac{9}{19.29}+\frac{9}{29.39}+....+\frac{9}{1999.2009}\)

\(A=\frac{1}{19}+\left(\frac{9}{19.29}+\frac{9}{29.39}+.....+\frac{9}{1999.2009}\right)\)

\(A=\frac{1}{19}+\frac{9}{10}\left(\frac{10}{19.29}+\frac{10}{29.39}+....+\frac{10}{1999.2009}\right)\)

\(A=\frac{1}{19}+\frac{9}{10}\left(\frac{1}{19}-\frac{1}{29}+\frac{1}{29}-\frac{1}{39}+.....+\frac{1}{1999}-\frac{1}{2009}\right)\)

\(A=\frac{1}{19}+\frac{9}{10}\left(\frac{1}{19}-\frac{1}{2009}\right)\)

\(A=\frac{1}{19}+\frac{9}{10}.\frac{1990}{38171}\)

\(A=\frac{1}{19}+\frac{1791}{38171}\)

\(A=\frac{200}{2009}\)

25 tháng 1 2017

A = 200/2009

đúng 100%, mk thi r` nhưng làm biếng giải

15 tháng 7 2018

\(\frac{1}{19}+\frac{9}{19.29}+\frac{9}{29.39}+...+\frac{9}{1999.2009}\)

\(=\frac{1}{19}+\frac{9}{10}\left(\frac{10}{19.29}+\frac{10}{29.39}+...+\frac{10}{1999.2009}\right)\)

\(=\frac{1}{19}+\frac{9}{10}.\left(\frac{1}{19}-\frac{1}{29}+\frac{1}{29}-\frac{1}{39}+...+\frac{1}{1999}-\frac{1}{2009}\right)\)

\(=\frac{1}{19}+\frac{9}{10}.\left(\frac{1}{19}-\frac{1}{2009}\right)\)

b tự làm nốt nhé

15 tháng 7 2018

\(\frac{1}{9.19}+\frac{1}{19.29}+\frac{1}{29.39}+...+\frac{1}{1999.2009}\)

\(=\frac{1}{10}\times\left(\frac{10}{9.19}+\frac{10}{19.29}+\frac{10}{29.39}+...+\frac{10}{1999.2009}\right)\)

\(=\frac{1}{10}\times\left(\frac{1}{9}-\frac{1}{19}+\frac{1}{19}-\frac{1}{29}+\frac{1}{29}-\frac{1}{39}+...+\frac{1}{1999}-\frac{1}{2009}\right)\)

\(=\frac{1}{10}\times\left(\frac{1}{9}-\frac{1}{2009}\right)\)

\(=\frac{1}{10}\times\frac{2000}{18081}\)

\(=\frac{200}{18081}\)

_Chúc bạn học tốt_

9 tháng 9 2018

\(A=\frac{1}{19}+\frac{9}{10}\left(\frac{10}{19.29}+\frac{10}{29.39}+...+\frac{10}{1999.2009}\right)\)

\(A=\frac{1}{19}+\frac{9}{10}\left(\frac{1}{19}-\frac{1}{29}+\frac{1}{29}-\frac{1}{39}+...+\frac{1}{1999}-\frac{1}{2009}\right)\)

\(A=\frac{1}{19}+\frac{9}{10}\left(\frac{1}{9}-\frac{1}{2009}\right)\)

\(A=\frac{1}{19}+\frac{9}{10}\left(\frac{2000}{18081}\right)\)

\(A=\frac{1}{19}+\frac{200}{2009}\)

\(A=\frac{5809}{38171}\)

MK ko chắc nhé =v ( mấy bước quy đồng lằng nhằng ko làm âu )

22 tháng 5 2017

Ta có:

\(A=\dfrac{1}{19}+\dfrac{9}{19.29}+\dfrac{9}{29.39}+...+\) \(\dfrac{9}{1999.2009}\)

\(=\dfrac{1}{19}+\) \(\left(\dfrac{9}{19.29}+\dfrac{9}{29.39}+...+\dfrac{9}{1999.2009}\right)\)

\(=\dfrac{1}{19}\) \(+\) \(\dfrac{9}{10}\left(\dfrac{10}{19.29}+\dfrac{10}{29.39}+...+\dfrac{10}{1999.2009}\right)\)

\(=\dfrac{1}{19}+\dfrac{9}{10}\left(\dfrac{1}{19}-\dfrac{1}{29}+\dfrac{1}{29}-\dfrac{1}{39}+...+\dfrac{1}{1999}-\dfrac{1}{2009}\right)\)

\(=\dfrac{1}{19}+\dfrac{9}{10}\left(\dfrac{1}{19}-\dfrac{1}{2009}\right)=\dfrac{200}{2009}\)

Vậy \(A=\dfrac{200}{2009}\)

1 tháng 3 2017

tr tốc độ kinh khủng!!!! ms có 4p mà p vừa đánh máy vừa suy nghĩ hả ? BÁI PHỤC !!!

23 tháng 2 2017

\(\frac{1}{19}+\frac{9}{19.29}+\frac{9}{29.39}+...+\frac{9}{1999.2009}\)

= \(\frac{1}{19}+\left(\frac{9}{19.29}+\frac{9}{29.39}+...+\frac{9}{1999.2009}\right)\)

= \(\frac{1}{19}+\frac{9}{10}\left(\frac{10}{19.29}+\frac{10}{29.39}+...+\frac{10}{1999.2009}\right)\)

= \(\frac{1}{19}+\frac{9}{10}\left(\frac{1}{19}-\frac{1}{29}+\frac{1}{29}-\frac{1}{39}+...+\frac{1}{1999}-\frac{1}{2009}\right)\)

= \(\frac{1}{19}+\frac{9}{10}\left(\frac{1}{19}-\frac{1}{2009}\right)\)

= \(\frac{1}{19}+\frac{9}{10}.\frac{1990}{38171}\)

= \(\frac{1}{19}+\frac{1791}{38171}\)

= \(\frac{200}{2009}\)

21 tháng 5 2017

Lưu An

\(A=\dfrac{1}{19}+\left(\dfrac{9}{19\cdot29}+\dfrac{9}{29\cdot39}+...+\dfrac{9}{1999\cdot2009}\right)\)

\(A=\dfrac{1}{19}+\dfrac{9}{10}\left(\dfrac{10}{19\cdot29}+\dfrac{10}{29\cdot39}+...+\dfrac{10}{1999\cdot2009}\right)\)

\(A=\dfrac{1}{19}+\dfrac{9}{10}\left(\dfrac{1}{19}-\dfrac{1}{29}+\dfrac{1}{29}-\dfrac{1}{39}+...+\dfrac{1}{1999}-\dfrac{1}{2009}\right)\)

\(A=\dfrac{1}{19}+\dfrac{9}{10}\left(\dfrac{1}{19}-\dfrac{1}{2009}\right)\)

\(A=\dfrac{1}{19}+\dfrac{9}{10}\cdot\dfrac{1990}{38171}\)

\(A=\dfrac{1}{19}+\dfrac{1791}{38171}\)

\(A=\dfrac{200}{2009}\)

21 tháng 5 2017

B=1/19+(9/19.29+9/29.39+...+9/1999.2009)

B=1/19+9/10+(10/19.29+10/29.39+.....+10/1999.2009

B=1/19+9/10+(1/19-1/29+1/29-1/39+....+1/1999-1/2009)

B=1/19+9/10+(1/19-1/2009)

B=1/19+9/10.1990/38171

B=1/19+1791/38171

B=200/2009

Vậy B= 200/2009