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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

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

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

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

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

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

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

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

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

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

6 tháng 2 2017

\(A=\frac{1}{19}+\frac{9}{10}\left(\frac{10}{19.29}+\frac{10}{29.39}+...+\frac{10}{1999.2000}\right)\)

\(=\frac{1}{19}+\frac{9}{10}\left(\frac{1}{19}-\frac{1}{29}+\frac{1}{29}-\frac{1}{39}+...+\frac{1}{1999}-\frac{1}{2000}\right)\)

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

\(=\frac{1}{19}+\frac{9}{10}\left(\frac{1990}{38171}\right)\)\(=\frac{1}{19}+\frac{1791}{38171}\)\(=\frac{200}{2009}\)

6 tháng 2 2017

Nhớ k mik nha bạn Capricorn

8 tháng 2 2017

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

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

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

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

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

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

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

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

8 tháng 2 2017

Thanks bạn nhiều nha! Chúc bạn học tốt ! haha

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

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

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

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

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_