\(C=\dfrac{1}{2}+\dfrac{1}{2^3}+\dfrac{1}{2^5}+...+\dfrac{1}{2^{99}}\)
\(\Rightarrow4C=2+\dfrac{1}{2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{97}}\)
\(\Rightarrow3C=4C-C=2+\dfrac{1}{2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{97}}-\dfrac{1}{2}-\dfrac{1}{2^3}-...-\dfrac{1}{2^{99}}=2-\dfrac{1}{2^{99}}\)
\(\Rightarrow C=\dfrac{2-\dfrac{1}{2^{99}}^{ }}{3}\)
