2.7 Taylorの定理

(a) $${\sum_{n=0}^{\infty}(-1)^n x^{n}}$$ (b) $${\sum_{n=0}^{\infty}x^{2n}}$$ (c) $${1 + \frac{1}{2}x^2 + \frac{3}{8}x^4 + \cdots + \frac{1\cdot 3 \cdot 5 \cdots (2n-1)}{2^n n!}x^{2n} + \cdots}$$

(d) $${1 - \frac{1}{2}x^2 - \frac{1}{8}x^4 - \cdots - \frac{1\cdot 3 \cdot 5 \cdots (2n-3)}{2^n n!}x^{2n} + \cdots}$$