ex=1+x+12!x2+⋯1n!xn+o(xn)e^x=1+x+\dfrac{1}{2!}x^2+\cdots\dfrac{1}{n!}x^n+o(x^n)ex=1+x+2!1x2+⋯n!1xn+o(xn)
sinx=x−13!x3+⋯+(−1)n(2n+1)!x2n+1+o(x2n+1)\sin x=x-\dfrac{1}{3!}x^3+\cdots+\dfrac{(-1)^n}{(2n+1)!}x^{2n+1}+o(x^{2n+1})sinx=x−3!1x3+⋯+(2n+1)!(−1)nx2n+1+o(x2n+1)
cosx=1−12!x2+14!x4+⋯+(−1)n(2n)!x2n+o(x2n)\cos x=1-\dfrac{1}{2!}x^2+\dfrac{1}{4!}x^4+\cdots+\dfrac{(-1)^n}{(2n)!}x^{2n}+o(x^{2n})cosx=1−2!1x2+4!1x4+⋯+(2n)!(−1)nx2n+o(x2n)
ln(1+x)=x−x22+x33−⋯+(−1)n−1nxn+o(xn)\ln(1+x)=x-\dfrac{x^2}{2}+\dfrac{x^3}{3}-\cdots+\dfrac{(-1)^{n-1}}{n}x^n+o(x^n)ln(1+x)=x−2x2+3x3−⋯+n(−1)n−1xn+o(xn)
(1+x)a=1+ax+a(a−1)2!x2+⋯+a(a−1)⋯(a−n+1)n!+o(xn)(1+x)^a=1+ax+\dfrac{a(a-1)}{2!}x^2+\cdots+\dfrac{a(a-1)\cdots(a-n+1)}{n!}+o(x^n)(1+x)a=1+ax+2!a(a−1)x2+⋯+n!a(a−1)⋯(a−n+1)+o(xn)
11+x=1−x+x2−⋯+(−1)nxn+o(xn)\dfrac{1}{1+x}=1-x+x^2-\cdots+(-1)^nx^n+o(x^n)1+x1=1−x+x2−⋯+(−1)nxn+o(xn)
11−x=1+x+x2+⋯+xn+o(xn)\dfrac{1}{1-x}=1+x+x^2+\cdots+x^n+o(x^n)1−x1=1+x+x2+⋯+xn+o(xn)
扫一扫
3265
被折叠的 条评论
为什么被折叠?
到【灌水乐园】发言
