级数求和问题

f(x) = ∑x^n/n!
∫f(x) dx = ∫∑x^n/n!dx
∫f(x) dx = ∑∫x^n/n!dx = ∑ x^(n+1)/(n+1)!= f(x) - 1
f(x) = e^x+C
f(0) = 1 (注：0^0/0!= 1)
f(x) = e^x