00:01
So for this question, we are asked to find the sum.
00:03
So we have k equals zero all the way up until k equals three.
00:07
So pretty much all we have to do is substitute k in for zero, one, two, and three, and then add all of those together.
00:14
So i'll just make a quick table here.
00:16
So we have when k is zero, one, two, and three.
00:23
And so remember that three is because this is the number here.
00:26
So pretty much if it was like five, for example, we would go up all the way until.
00:30
5 and add all those, you know, terms together.
00:33
So in the case where k equals 0, we have 1 over 0 squared plus 1.
00:40
So 1 over 0 squared plus 1 is just going to be 1 over 1.
00:45
Then we have 1 over k is going to be 1.
00:49
So we have 1 squared plus 1.
00:50
That's 1 1 half.
00:52
And then we have 2 as k.
00:55
So k squared, 2 squared plus 1 is 5.
00:58
So we have 1 over 4 plus 1.
01:00
1, which is 5...