00:01
Hello, so given our series, checking for absolute convergence, we want to check if the, here, looking at the sum of the absolute value of our series of the sum, just going n going from 0 to infinity, of just the absolute value of n squared over n squared plus 1, we can notice that the absolute value of n squared over n squared plus 1 is equal to just n squared over n squared plus 1, which then simplifies to a fraction that just approaches 1 as n becomes large.
00:33
And to verify then whether the series converges or diverges, we can notice that the limit as n tends to infinity of just n squared over n squared plus 1 is actually going to be equal to just 1.
00:49
And then since the series consists of terms that do not tend to 0, according to the basic divergence test, the series would diverge.
01:00
Therefore, the original series, we can say, is not absolutely convergent.
01:09
Then to test for conditional convergence, we check if the original alternating series converges even though its absolute series does not...