Use the Comparison Test to determine the convergence or divergence of ∞Σ(n=1) 1/n!.?
回答 (1)
2016-03-28 7:44 am
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
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
收錄日期: 2021-04-30 12:03:21
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