00:01
In this question, we are asked to test the given series for convergence.
00:05
We'll rewrite this as the series negative 1 to the n multiplied by 1 over n times 5 to the n, n from 1 to infinity.
00:16
Recall that an alternating series is the series of the form negative 1 to the n, bn, n from 1 to infinity.
00:29
This is the general formula for an alternating series.
00:32
In our case, bn equals 1 over n times 5 to the n.
00:38
So our series is an alternating series, and that means we can apply the alternating series test.
00:57
We need to calculate the limit of bn as n goes to infinity, and when n goes to infinity, the denominator goes to infinity, and 1 over infinity is 0.
01:15
And also, note that n plus 1 multiplied by 5 to the n plus 1 is greater than n multiplied by 5 to the n, right? for n greater or equal than 1.
01:34
If we take the reciprocals, we'll get the sign of the inequality will change for all n greater or equal than 1...