Geometric series/R/Even and odd indices/Exercise

Let ${}x\in \mathbb {R}$ , ${}\vert {x}\vert <1$. Determine (in dependence of ${}x$) the sum of the two series

$\sum _{k=0}^{\infty }x^{2k}{\text{ and }}\sum _{k=0}^{\infty }x^{2k+1}.$

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