Ratio Test

Examples 4.2.16(e):

Use the ratio test and the divergence test to show that for any fixed number a
an/n! = 0

According to the ratio test the series


converges absolutely, as you can readily check. But then, by the divergence theorem, the sequence


must converge to zero.

This is a pretty round-about proof with heavy artillery. A simple induction proof might be successful, too.

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