5.2.1

[STARTS AT 8:03]

Instructor: Determine whether this series converges. All right, well, that series-- first, I'm going to rewrite this. This is 1 plus 1 over n. All right. So S1-- our terms, our first term is 1 and 1/2. Our second term is 1 and 1/2-- hold on. Oh, actually the first term is 2. Second term is 2 plus 1.5. 2, plug-in the value of 2. That's 1 and 1/2, so this is a total of 3 and 1/2. OK, we do 2 plus-- or 3.5 plus 4/3. That's going to be about 4.83. 

OK. All right, so-- and I just did-- that was actually the sum that I just did. So let's write that differently. S1, S2, S3. So our terms are 2, 2 plus 1.5, which is 3.5. 2 plus 1.5 plus, plugging in a 3, we get 4/3, so 1.3 repeating, which is 4.83. OK. So I actually just did too much work. That'll be a better way to organize that. 

OK. So let's see if we can compare. These don't appear they're going to have any sign of stopping either. The first one is greater than 1. The second term is greater than 2. The third one is greater than 3. So why don't we say that Sk is greater than k. Now Sk goes to infinity, that puts Sk diverging to infinity, which means that our sum, 1 to infinity of n plus 1 over n diverges.

[ENDS AT 10:20]