\(A=\dfrac{1}{19}+\left(\dfrac{9}{19\cdot29}+\dfrac{9}{29\cdot39}+...+\dfrac{9}{1999\cdot2009}\right)\)
\(A=\dfrac{1}{19}+\dfrac{9}{10}\left(\dfrac{10}{19\cdot29}+\dfrac{10}{29\cdot39}+...+\dfrac{10}{1999\cdot2009}\right)\)
\(A=\dfrac{1}{19}+\dfrac{9}{10}\left(\dfrac{1}{19}-\dfrac{1}{29}+\dfrac{1}{29}-\dfrac{1}{39}+...+\dfrac{1}{1999}-\dfrac{1}{2009}\right)\)
\(A=\dfrac{1}{19}+\dfrac{9}{10}\left(\dfrac{1}{19}-\dfrac{1}{2009}\right)\)
\(A=\dfrac{1}{19}+\dfrac{9}{10}\cdot\dfrac{1990}{38171}\)
\(A=\dfrac{1}{19}+\dfrac{1791}{38171}\)
\(A=\dfrac{200}{2009}\)
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
