\(D=1+3^2+3^4+...+3^{98}+3^{100}\)
\(3^2D=3^2\left(1+3^2+3^4+...+3^{98}+3^{100}\right)\)
\(9D=3^2+3^4+3^6+...+3^{100}+3^{102}\)
\(9D-D=\left(3^2+3^4+...+3^{102}\right)-\left(1+3^2+...+3^{100}\right)\)
\(8D=3^{102}-1\Rightarrow D=\dfrac{3^{102}-1}{8}\)