Monday, June 20, 2016

real analysis - Show that evarepsilon|x|varepsilon grows faster than suminftyk=0|x|2k/(k!)2

I am wondering whether we have for f(x):=k=0|x|2k(k!)2 that



lim
for any \varepsilon>0?



I assume that this is true as factorials should somehow outgrow powers, but I do not see how to show this rigorously?



Does anybody have an idea?

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