The Ratio Test


The general term of the series is tex2html_wrap_inline52 , thus the absolute ratios have the form:

displaymath46

Now since tex2html_wrap_inline54 ,

displaymath47

we can continue computing the limit of the absolute ratios as

displaymath48

no matter which value we consider for x. Since 0<1, the ratio test lets us conclude that this series converges for all real x. The radius of convergence of this series is tex2html_wrap_inline62 .


Helmut Knaust
Fri Jul 12 16:31:37 MDT 1996

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