anonymous
  • anonymous
Does the series converge or diverge? Summation of n!/5^n
Mathematics
katieb
  • katieb
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dumbcow
  • dumbcow
i would say diverge factorials grow much faster than exponential functions
dumbcow
  • dumbcow
if you evaluate sum even for only first 50 terms its already at like 3 X10^29
anonymous
  • anonymous
well, you can evaluate it using the ratio test, but I'm not sure how to do all of the steps :/

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anonymous
  • anonymous
Yeah ratio test confirms divergence. In the ration test you have (n+1)!/5^(n+1) divided by original one. This breaks down to (n+1)/5. Take limit. It goes to infinity. Infinity>0 diverge

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