\(D=1-3+3^2-3^3+3^4-3^5+...+3^{98}-3^{99}+3^{100}\)
\(3D=3\left(1-3+3^2-3^3+3^4-3^5+...+3^{98}-3^{99}+3^{100}\right)\)
\(3D=3-3^2+3^3-3^4+3^5-3^6+...+3^{99}-3^{100}+3^{101}\)
\(3D+D=\left(3-3^2+3^3-3^4+3^5-3^6+...+3^{99}-3^{100}+3^{101}\right)\)
\(+\left(1-3+3^2-3^3+3^4-3^5+...+3^{98}-3^{99}+3^{100}\right)\)
\(4D=3^{101}+1\) \(\Rightarrow D=\frac{3^{101}+1}{4}\)