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Apply the ratio test and state its conclusion:

Apply the ratio test and state its conclusion: āˆ‘ n=1, āˆž (n)^100/(100)^n
XApply the ratio test and state its conclusion:

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Andre W. | Friendly tutor for ALL math and physics coursesFriendly tutor for ALL math and physics ...
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We need to look at the ratio of successive terms, an+1/an, and check if in the limit nā†’āˆž the ratio is > or < than 1:
((n+1)100/100n+1)/(n100/100n) = ((n+1)100/n100)/(100n+1/100n) = (1+1/n)100/100
The limit is 1/100, which is less than 1, therefore by the ratio test, the series converges.
 
Conceptually: the exponential function in the denominator increases much faster than the power function in the numerator, so their ratio gets small fast.