Search 80,000+ tutors
Ask a question
0 0

Apply the ratio test and state its conclusion:

Tutors, please sign in to answer this question.

1 Answer

We need to look at the ratio of successive terms, an+1/an, and check if in the limit n→∞ 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.