Find the Taylor series for 1x\frac{1}{x}x1 centered at a=2a=2a=2.
∑n=0∞(−1)n(x−2)n2n+1\sum_{n=0}^{\infty} \frac{(-1)^n (x-2)^n}{2^{n+1}}∑n=0∞2n+1(−1)n(x−2)n
∑n=0∞(x−2)n2n\sum_{n=0}^{\infty} \frac{(x-2)^n}{2^n}∑n=0∞2n(x−2)n
∑n=0∞(−1)n(x−2)n2n\sum_{n=0}^{\infty} \frac{(-1)^n (x-2)^n}{2^n}∑n=0∞2n(−1)n(x−2)n
∑n=0∞(x−2)n2n+1\sum_{n=0}^{\infty} \frac{(x-2)^n}{2^{n+1}}∑n=0∞2n+1(x−2)n