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    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.