a: \(=\dfrac{3}{5}\left(\dfrac{5}{1\cdot6}+\dfrac{5}{6\cdot11}+...+\dfrac{5}{496\cdot501}\right)\)
=3/5(1-1/6+1/6-1/11+...+1/496-1/501)
=3/5*500/501=300/501=100/167
b: \(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}\)
=1/2-1/100
=50/100-1/100=49/100
