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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
\(A=\frac{1}{19}+\frac{9}{10}\left(\frac{10}{19.29}+\frac{10}{29.39}+...+\frac{10}{1999.2000}\right)\)
\(=\frac{1}{19}+\frac{9}{10}\left(\frac{1}{19}-\frac{1}{29}+\frac{1}{29}-\frac{1}{39}+...+\frac{1}{1999}-\frac{1}{2000}\right)\)
\(=\frac{1}{19}+\frac{9}{10}\left(\frac{1}{19}-\frac{1}{2000}\right)\)
\(=\frac{1}{19}+\frac{9}{10}\left(\frac{1990}{38171}\right)\)\(=\frac{1}{19}+\frac{1791}{38171}\)\(=\frac{200}{2009}\)
BN
8 tháng 2 2017
A = \(\frac{1}{19}+\frac{9}{19.29}+\frac{9}{29.39}+...+\frac{9}{1999.2009}\)
\(=\frac{1}{19}+\left(\frac{9}{19.29}+\frac{9}{29.39}+...+\frac{9}{1999.2009}\right)\)
\(=\frac{1}{19}+9\left(\frac{1}{19.29}+\frac{1}{29.39}+...+\frac{1}{1999.2009}\right)\)
\(=\frac{1}{19}+9.\frac{1}{10}\left(\frac{1}{19}-\frac{1}{29}+\frac{1}{29}-\frac{1}{39}+...+\frac{1}{1999}-\frac{1}{2009}\right)\)
\(=\frac{1}{19}+\frac{9}{10}\left(\frac{1}{19}-\frac{1}{2009}\right)\)
\(=\frac{1}{19}+\frac{9}{10}.\frac{1990}{38171}\)
\(=\frac{1}{19}+\frac{1791}{38171}\)
\(=\frac{200}{2009}\)
1
19 tháng 9 2021
\(\dfrac{1}{19}+\dfrac{9}{19\cdot29}+...+\dfrac{9}{1999\cdot2009}\)
\(=\dfrac{1}{19}+\dfrac{9}{10}\left(\dfrac{10}{19\cdot29}+...+\dfrac{10}{1999\cdot2009}\right)\)
\(=\dfrac{1}{19}+\dfrac{9}{10}\left(\dfrac{1}{19}-\dfrac{1}{2009}\right)\)
\(=\dfrac{1}{19}+\dfrac{1791}{38171}=\dfrac{200}{2009}\)
G6
3
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_
\(A=\frac{1}{19}+\frac{9}{19.29}+\frac{9}{29.39}+....+\frac{9}{1999.2009}\)
\(A=\frac{1}{19}+\left(\frac{9}{19.29}+\frac{9}{29.39}+.....+\frac{9}{1999.2009}\right)\)
\(A=\frac{1}{19}+\frac{9}{10}\left(\frac{10}{19.29}+\frac{10}{29.39}+....+\frac{10}{1999.2009}\right)\)
\(A=\frac{1}{19}+\frac{9}{10}\left(\frac{1}{19}-\frac{1}{29}+\frac{1}{29}-\frac{1}{39}+.....+\frac{1}{1999}-\frac{1}{2009}\right)\)
\(A=\frac{1}{19}+\frac{9}{10}\left(\frac{1}{19}-\frac{1}{2009}\right)\)
\(A=\frac{1}{19}+\frac{9}{10}.\frac{1990}{38171}\)
\(A=\frac{1}{19}+\frac{1791}{38171}\)
\(A=\frac{200}{2009}\)
A = 200/2009
đúng 100%, mk thi r` nhưng làm biếng giải