# Series defined recursively

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1) The terms of series are defined recursively by the equations:

a1=2 a(n+1)=(5n+1)/(4n+3)an

Determine whether ?" an converges or diverges

2) a) Show that ?" (from n=0 to infinity) [x^n/n!]converges for all x

b) Deduce that lim ( n--> infinity)[x^n/n!] = 0 for all x.

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#### Solution Summary

This is a series of problems with convergent and divergent series.

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