$\begin{array}{l}1)\\D=\dfrac2{1.3}+\dfrac3{3.6}+\dfrac4{6.10}+\dfrac5{10.15}+\dfrac6{15.21}\\\to D=1-\dfrac13+\dfrac13-\dfrac16+\dfrac16-\dfrac1{10}+\dots+\dfrac1{15}-\dfrac1{21}\\\to D=1-\dfrac1{21}\\\to D=\dfrac{21}{21}-\dfrac1{21}\\\to D=\dfrac{20}{21}\\\,\\2)\\S=\dfrac{3}{1.4}+\dfrac3{4.7}+\dfrac3{7.10}+\dots+\dfrac3{n(n+3)}\\\to S=1-\dfrac14+\dfrac14-\dfrac17+\dfrac17-\dfrac1{10}+\dots+\dfrac1{n}-\dfrac1{n+3}\\\to S=1-\dfrac1{n+3}\\\text{- Do $\dfrac1{n+3}>0$}\\\to 1-\dfrac1{n+3}<1\\\to S<1 \end{array}$
