What is the Taylor series of f(x)=cos(x)f(x) = \cos(x)f(x)=cos(x) centered at a=π2a = \frac{\pi}{2}a=2π?
∑n=0∞(−1)n+1(x−π/2)2n+1(2n+1)!\sum_{n=0}^{\infty} \frac{(-1)^{n+1} (x-\pi/2)^{2n+1}}{(2n+1)!}∑n=0∞(2n+1)!(−1)n+1(x−π/2)2n+1
∑n=0∞(−1)n(x−π/2)2n(2n)!\sum_{n=0}^{\infty} \frac{(-1)^n (x-\pi/2)^{2n}}{(2n)!}∑n=0∞(2n)!(−1)n(x−π/2)2n
∑n=0∞(x−π/2)2n+1(2n+1)!\sum_{n=0}^{\infty} \frac{(x-\pi/2)^{2n+1}}{(2n+1)!}∑n=0∞(2n+1)!(x−π/2)2n+1
∑n=0∞(−1)n+1(x−π/2)2n(2n)!\sum_{n=0}^{\infty} \frac{(-1)^{n+1} (x-\pi/2)^{2n}}{(2n)!}∑n=0∞(2n)!(−1)n+1(x−π/2)2n