$a,\dfrac{6}{1.2}$ $+\dfrac{6}{2.3}+$ $\dfrac{6}{3.4}$ $+\dfrac{6}{4.5}+$ $...+\dfrac{6}{98.99}$ $+\dfrac{6}{99.100}$
$=6(\dfrac{1}{1.2}$ $+\dfrac{1}{2.3}+$ $\dfrac{1}{3.4}$ $+\dfrac{1}{4.5}+$ $...+\dfrac{1}{98.99}$ $+\dfrac{1}{99.100})$
$=6(1-\dfrac{1}{2}$ $+\dfrac{1}{2}-$ $\dfrac{1}{3}$ $+\dfrac{1}{3}+$ $...-\dfrac{1}{99}$ $+\dfrac{1}{99}-\dfrac{1}{100})$
$=6(1-\dfrac{1}{100})$
$=6.\dfrac{99}{100}$
$=\dfrac{297}{50}$
$b,\dfrac{5}{1.4}$ $+\dfrac{5}{4.7}+$ $\dfrac{5}{7.10}$ $+\dfrac{5}{10.14}+$ $...+\dfrac{5}{94.97}$ $+\dfrac{5}{97.100}$
$=\dfrac35(\dfrac{3}{1.4}$ $+\dfrac{3}{4.7}+$ $\dfrac{3}{7.10}$ $+\dfrac{3}{10.14}+$ $...+\dfrac{3}{94.97}$ $+\dfrac{3}{97.100})$
$=\dfrac35(1-\dfrac{1}{4}$ $+\dfrac{1}{4}-$ $\dfrac{1}{7}$ $+\dfrac{1}{7}+$ $...-\dfrac{1}{97}$ $+\dfrac{1}{97}-\dfrac{1}{100})$
$=\dfrac35(1-\dfrac{1}{100})$
$=\dfrac35.\dfrac{99}{100}$
$=\dfrac{297}{500}$
