If ∑n=0∞anxn\sum_{n=0}^{\infty} a_n x^n∑n=0∞anxn converges to 12−x\frac{1}{2-x}2−x1 for ∣x∣<2|x| < 2∣x∣<2, what is the expression for ana_nan?
an=2−na_n = 2^{-n}an=2−n
an=2−(n+1)a_n = 2^{-(n+1)}an=2−(n+1)
an=(−1)n2−na_n = (-1)^n 2^{-n}an=(−1)n2−n
an=2na_n = 2^nan=2n