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Determine whether the statement is true or false.$\newline$$f(x)=\frac{1}{1-x}=\sum_{n=0}^{\infty} x^{n}$ and $g(x)=\frac{1}{1-x^{2}}=\sum_{n=0}^{\infty} x^{2 n}$, then $f(x) g(x)=\sum_{n=0}^{\infty} x^{n} x^{2 n}=\sum_{n=0}^{\infty} x^{3 n}$$\newline$True$\newline$False