Interactive Real Analysis - part of MathCS.org

Next | Previous | Glossary | Map | Discussion

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

an/n!

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

|a|n/n!

must converge to zero.

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

Next | Previous | Glossary | Map | Discussion