收敛半径 R = lim(n+1)3^(n+1)/(n3^n) = 3收敛域 x∈[-3,3)S(x) = ∑x^n/(n3^n), S(0) = 0S'(x) = ∑x^(n-1)/3^n = ∑(1/3)(x/3)^(n-1) = (1/3)/(1-x/3), x∈[-3,3)S(x) = ∫<0, x> S'(t)dt +S(0) = ∫<0, x> (1/3)dt/(1-t/3) = -ln(1-x/3), x∈[-3,3)∑(-1)^(n+1)/(n3^n)= -∑(-1)^n/(n3^n)= -S(-1) = ln(1+1/3) = 2ln2-ln3