lim(n→∞)|[(2n+3)x^(2n+2)/(n+1)!]/[(2n+1)x^(2n)/n!]|=0x∈(-∞,+∞)拆项【e^x=∑(n=0~+∞)(1/n!)x^n=1+x+x^2/2!+x^3/3!+...+x^n/n!+...】令x^2=y∵∑(n=1~+∞)[(2n+1)/n!]y^n=2∑(n=1~+∞)[1/(n-1)!]y^n+∑(n=1~+∞)(1...