00:01
So in this problem, we're asked to use any method to determine whether the series converges, and we're given the sum from 1 to infinity of k squared over k -kube plus 1.
00:10
So why don't we utilize the limit comparison test, and we can compare it this series to the series the sum from 1 to infinity of k squared over k -c cubed, or which this is just equal to the sum from one to infinity of 1 over k, which we know diverges by the p test.
00:43
Okay, so we can do the limit comparison test.
00:49
So we take the limit as k approaches infinity of a subk over b subk, where we can let the original sequence be a subk, and we'll let this one be b sub k.
01:10
So this is equal to the limit as k approaches infinity of k squared over k cubed plus one over k squared over k cubed.
01:31
Okay, we can multiply by the reciprocal to get the limit as k approaches infinity of k squared over k cubed plus one times k cubed over k squared...