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

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

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

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

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

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

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

\(\Leftrightarrow\text{ }A=\frac{9}{9.19}+\frac{9}{19.29}+\frac{9}{29.39}+......+\frac{9}{1999.2000}\)

\(\Rightarrow\text{ }A=\frac{9}{10}.\left(\frac{10}{9.19}+\frac{10}{19.29}+\frac{10}{29.39}+......+\frac{10}{1999.2009}\right)\)

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

\(\Rightarrow\text{ }A=\frac{9}{10}.\left(\frac{1}{9}-\frac{1}{2009}\right)\)

\(\Rightarrow\text{ }A=\frac{9}{10}.\frac{2000}{18081}=\frac{200}{2009}\)

thank

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

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

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

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

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!

Lưu An

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

mk ko bt 123