題目 Problem Find the power series centered at −2-2−2 that is equal to f(x)=11−x.f(x)=\frac{1}{1-x}.f(x)=1−x1. (a) ∑n=0∞(x+2)n2n\displaystyle \sum_{n=0}^{\infty}\frac{(x+2)^n}{2^n}n=0∑∞2n(x+2)n (b) ∑n=0∞(x+2)n2n+1\displaystyle \sum_{n=0}^{\infty}\frac{(x+2)^n}{2^{n+1}}n=0∑∞2n+1(x+2)n (c) ∑n=0∞(x+2)n3n\displaystyle \sum_{n=0}^{\infty}\frac{(x+2)^n}{3^n}n=0∑∞3n(x+2)n (d) ∑n=0∞(x+2)n3n+1\displaystyle \sum_{n=0}^{\infty}\frac{(x+2)^n}{3^{n+1}}n=0∑∞3n+1(x+2)n (e) None of the above. 解答 待補。
