Find the Taylor series for f(x)=1xf(x) = \frac{1}{x}f(x)=x1 centered at a=2a=2a=2.
∑n=0∞(−1)n2n+1(x−2)n\sum_{n=0}^{\infty} \frac{(-1)^n}{2^{n+1}} (x-2)^n∑n=0∞2n+1(−1)n(x−2)n
∑n=0∞12n+1(x−2)n\sum_{n=0}^{\infty} \frac{1}{2^{n+1}} (x-2)^n∑n=0∞2n+11(x−2)n
∑n=0∞(−1)n2n(x−2)n\sum_{n=0}^{\infty} \frac{(-1)^n}{2^n} (x-2)^n∑n=0∞2n(−1)n(x−2)n
∑n=0∞(−1)nn!2n+1(x−2)n\sum_{n=0}^{\infty} \frac{(-1)^n n!}{2^{n+1}} (x-2)^n∑n=0∞2n+1(−1)nn!(x−2)n