Which is the Maclaurin series for f(x)=11−x=(1−x)−1/2f(x) = \frac{1}{\sqrt{1-x}} = (1-x)^{-1/2}f(x)=1−x1=(1−x)−1/2?
∑n=0∞(2n)!22n(n!)2xn\sum_{n=0}^{\infty} \frac{(2n)!}{2^{2n}(n!)^2} x^n∑n=0∞22n(n!)2(2n)!xn
∑n=0∞(−1)n(2n)!22n(n!)2xn\sum_{n=0}^{\infty} \frac{(-1)^n (2n)!}{2^{2n}(n!)^2} x^n∑n=0∞22n(n!)2(−1)n(2n)!xn
∑n=0∞(2n−1)!!2n⋅n!xn\sum_{n=0}^{\infty} \frac{(2n-1)!!}{2^n \cdot n!} x^n∑n=0∞2n⋅n!(2n−1)!!xn
∑n=0∞(2n)xn\sum_{n=0}^{\infty} (2n) x^n∑n=0∞(2n)xn