What is the Maclaurin series for 31−2x\frac{3}{1-2x}1−2x3 (valid for ∣x∣<12|x| < \frac{1}{2}∣x∣<21)?
∑n=0∞3⋅2nxn\sum_{n=0}^{\infty} 3 \cdot 2^n x^n∑n=0∞3⋅2nxn
∑n=0∞3⋅2nxnn!\sum_{n=0}^{\infty} \frac{3 \cdot 2^n x^n}{n!}∑n=0∞n!3⋅2nxn
∑n=0∞3⋅(−2)nxn\sum_{n=0}^{\infty} 3 \cdot (-2)^n x^n∑n=0∞3⋅(−2)nxn
∑n=0∞3nxn2n\sum_{n=0}^{\infty} \frac{3^n x^n}{2^n}∑n=0∞2n3nxn