00:01
For this problem, our sequence is k squared over k factorial.
00:03
So, ak plus 1 minus ak will be equal to k plus 1 squared divided by k plus 1 factorial minus k squared over k factorial, which we can rewrite as k squared plus 2k plus 1 over k plus 1 over k times k plus 1.
00:28
Or excuse me, not that.
00:30
It would be k plus 1 times k factorial.
00:34
Then we have minus k squared over k factorial.
00:37
So we can get this over a common denominator by multiplying k squared over k factorial by k plus 1 over k plus 1.
00:45
So this becomes k squared plus 2k plus 1 minus k squared times k plus 1 divided by, all divided by, k plus 1 times k plus 1, k factorial, which we can then expand out that last term, writing this as k squared plus 2k, plus 1 minus k cubed, minus k squared...