lim a(n)/a(n+1) = lim n/(n+1) * (n+1)!/n! = +无穷大,所以收敛域是R因为e^x = 1+x/1! +x^2/2! +....de^x/dx = sum((n+1)x^n/n!)所以上述幂级数的和就是e^x