B=1/19 +9/19.29 + 9/39.49 +....+9/2009.2019 tính B
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27 tháng 12 2015
\(=\frac{1}{19}+\frac{9}{10}\left(\frac{1}{19}-\frac{1}{29}+\frac{1}{29}-\frac{1}{39}+...+\frac{1}{1999}-\frac{1}{2009}\right)\)
\(=\frac{1}{19}+\frac{9}{10}\left(\frac{1}{19}-\frac{1}{2009}\right)=\frac{1}{19}+\frac{9}{10}\cdot\frac{1990}{38171}=\frac{1}{19}+\frac{1791}{38171}=\frac{200}{2009}\)
TQ
0
1
19 tháng 9 2021
\(\dfrac{1}{19}+\dfrac{9}{19\cdot29}+...+\dfrac{9}{1999\cdot2009}\)
\(=\dfrac{1}{19}+\dfrac{9}{10}\left(\dfrac{10}{19\cdot29}+...+\dfrac{10}{1999\cdot2009}\right)\)
\(=\dfrac{1}{19}+\dfrac{9}{10}\left(\dfrac{1}{19}-\dfrac{1}{2009}\right)\)
\(=\dfrac{1}{19}+\dfrac{1791}{38171}=\dfrac{200}{2009}\)
P
2
19 tháng 9 2016
\(\text{Ta có : A = }\frac{1}{19}+\frac{9}{19.29}+\frac{9}{29.39}+.....+\frac{9}{1999.2009}\)
\(\Leftrightarrow\text{ }A=\frac{9}{9.19}+\frac{9}{19.29}+\frac{9}{29.39}+......+\frac{9}{1999.2000}\)
\(\Rightarrow\text{ }A=\frac{9}{10}.\left(\frac{10}{9.19}+\frac{10}{19.29}+\frac{10}{29.39}+......+\frac{10}{1999.2009}\right)\)
\(\Rightarrow\text{ }A=\frac{9}{10}.\left(\frac{1}{9}-\frac{1}{19}+\frac{1}{19}-\frac{1}{29}+......+\frac{1}{1999}-\frac{1}{2009}\right)\)
\(\Rightarrow\text{ }A=\frac{9}{10}.\left(\frac{1}{9}-\frac{1}{2009}\right)\)
\(\Rightarrow\text{ }A=\frac{9}{10}.\frac{2000}{18081}=\frac{200}{2009}\)
TZ
2
26 tháng 1 2017
\(=\frac{1}{19}+\frac{9}{10}\left(\frac{1}{19}-\frac{1}{29}+\frac{1}{29}-\frac{1}{39}+...+\frac{1}{1999}-\frac{1}{2009}\right)\)
\(=\frac{1}{19}+\frac{9}{10}\left(\frac{1}{19}-\frac{1}{2009}\right)\)
\(=\frac{1}{19}+\frac{9}{10}.\frac{1990}{38171}\)
\(=\frac{200}{2009}\)
26 tháng 1 2017
mình ko biết xin lỗi bạn nha!
mình ko biết xin lỗi bạn nha!
mình ko biết xin lỗi bạn nha!
mình ko biết xin lỗi bạn nha!
TT
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
TH
1
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 )
TT
1
Đề đúng phải là: \(B=\frac{9}{9\cdot19}+\frac{9}{19\cdot29}+\frac{9}{29\cdot39}+...+\frac{9}{2009\cdot2019}\) nhé :))
Ta có: \(B=\frac{9}{9\cdot19}+\frac{9}{19\cdot29}+\frac{9}{29\cdot39}+...+\frac{9}{2009\cdot2019}\)
\(\Rightarrow B=\frac{9}{10}\cdot\left(\frac{10}{9\cdot19}+\frac{10}{19\cdot29}+\frac{10}{29\cdot39}+...+\frac{10}{2009\cdot2019}\right)\)
\(\Rightarrow B=\frac{9}{10}\cdot\left(\frac{1}{9}-\frac{1}{19}+\frac{1}{19}-\frac{1}{29}+\frac{1}{29}-\frac{1}{39}+...+\frac{1}{2009}-\frac{1}{2019}\right)\)
\(\Rightarrow B=\frac{9}{10}\cdot\left(\frac{1}{9}-\frac{1}{2019}\right)=\left(\frac{9}{10}\cdot\frac{1}{9}\right)-\left(\frac{9}{10}\cdot\frac{1}{2019}\right)\)
\(\Rightarrow B=\frac{1}{10}-\frac{9}{20190}=\frac{2019}{20190}-\frac{9}{20190}=\frac{2010}{20190}=\frac{201}{2019}=\frac{67}{673}\)
Bạn kia viết đúng rùi mà.Bạn chỉ việc tách 1/19 ra thui