a: =1/2*2/3*3/4*..*99/100
=1/100
b: \(=\dfrac{7}{1\cdot4}+\dfrac{7}{4\cdot7}+...+\dfrac{7}{103\cdot106}\)
\(=\dfrac{7}{3}\left(\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+...+\dfrac{3}{103\cdot106}\right)\)
\(=\dfrac{7}{3}\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{103}-\dfrac{1}{106}\right)\)
\(=\dfrac{7}{3}\cdot\dfrac{105}{106}=\dfrac{245}{106}\)