$\begin{array}{l} S = 1.3 + 3.5 + 5.7 + ... + 101.103\\ \Rightarrow 6S = 1.3.6 + 3.5.\left( {7 - 1} \right) + 5.7\left( {9 - 3} \right) + ... + 101.103\left( {105 - 99} \right)\\ \Rightarrow 6S = 1.3.6 + 3.5.7 - 1.3.5 + 5.7.9 - 3.5.7 + ... + 101.103.105 - 101.103.99\\ \Rightarrow 6S = 1.3.6 - 1.3.5 + 101.103.105\\ \Rightarrow 6S = 1092318\\ \Rightarrow S = 182053 \end{array}$