Use the Comparison Test to determine the convergence or divergence of ∞Σ(n=1) 1/n!.?

Consider e = 1 + 1/1! + 1/2! + ... = ∑(n=0,∞) 1/n! ,
0 < ∑(n=1,∞) 1/n! < 1 + ∑(n=1,∞) 1/n!
0 < ∑(n=1,∞) 1/n! < ∑(n=0,∞) 1/n!
0 < ∑(n=1,∞) 1/n! < e
∴ Convergence