\begin{align*} 2.48484848... & = 2 + 0.48 + 0.0048 + 0.000048 + ...\\ & = 2 + 0.48(1 + 0.01 + 0.0001 + ... ) = 2 + 0.48 \sum_{k=0}^\infty (0.01)^k \end{align*}