Bài 7:
\(A=\dfrac{1}{3\cdot7}+\dfrac{1}{7\cdot11}+...+\dfrac{1}{199\cdot203}\)
\(=\dfrac{1}{4}\left(\dfrac{4}{3\cdot7}+\dfrac{4}{7\cdot11}+...+\dfrac{4}{199\cdot203}\right)\)
\(=\dfrac{1}{4}\left(\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+...+\dfrac{1}{199}-\dfrac{1}{203}\right)\)
\(=\dfrac{1}{4}\left(\dfrac{1}{3}-\dfrac{1}{203}\right)=\dfrac{1}{4}\cdot\dfrac{200}{609}=\dfrac{50}{609}\)
Bài 6:
\(A=a\cdot45,23+a\cdot80,54-a\cdot26,77+a\)
\(=a\cdot\left(45,23+80,54-26,77+1\right)\)
\(=a\cdot100\)
\(=99999\cdot100=9999900\)