This was one of the weirdest weeks I’ve had working through KA. I managed to get through 8 videos, 1 article (which contained 2 videos in itself) and 4 exercises, yet I barely reached 5 hours of studying in total. I only wrote 14 pages of notes, but almost everything I wrote I marked off as something I wanted to add to this post. I felt like I didn’t have much of a grasp on anything I worked through this week, yet every exercise I did I passed on my first attempt… 🤔 All in all, part of me is glad that I made progress through the vids/exercises but another side of me is bummed that I realized this week that I have a weaker grasp on the material in this unit than I thought I would have.

My week started working through the 2^nd exercise from the first section of this unit titled Convergent and Divergent Infinite Series. Including that exercise, I had two exercises to get through in that section which I got through on Tuesday. Both of these exercises helped me to get a better grasp on the notation used with this type of math. Below are 4 questions I worked through with the first 3 being from the 2^nd exercise in the section and the fourth being from the 3^rd exercise:

Question 1

Question 2

Question 3

Question 4

One thing that still hasn’t fully sunk in for me is that the notation used to state, ‘the sum of a series from a certain value in its index, b, to a certain value in its index, c, can be denoted as’ is  _bΣ^c A_n. To simplify its notation, it can also be written as S_c. You can see that I made a note of this at the bottom of the page from the third question. 

I was glad to work through the third exercise as it brought me back to using limits which I haven’t done in a long time and felt like I needed some practice with. As you can see from the fourth question above, I worked with limits by inputting infinity into the equations for different series and figuring out if the end result converged on a certain value or if it diverged. This exercise was pretty straightforward but got me thinking about the concept of limits, particularly when the limit of a variable approached infinity. 

On Wednesday I began the following section, Infinite Geometric Series. I skipped ahead in this section to an article titled Proof of Infinite Geometric Series Formula and wrote out the following notes:

I had a vague recollection of how these proofs work (although, as I mentioned, the second note isn’t technically a proof) so I didn’t find them too difficult to understand although I don’t really intuitively understand what each formula is saying just looking at it at face-value. This is because the notation S, A and r hasn’t sunk in for me yet. In any case, this section had 5 videos and 1 exercise that I worked through that all incorporated these two equations. Here’s a screen shot of the third video from this exercise and my note working through it below:

Here’s a question from the exercise in this section:

This is the longest KA answer I’ve ever seen!)

Question 5

I got through this section on Thursday and then began the following section titled n^th Term Test. This section only had 1 video and 1 exercise and, I’m not going to lie, I have no idea what’s going on in this section. Here’s a page from my notes that states the main concept from this section and an example question I worked on in the exercise:

Question 6

I’m not going to try an explain what’s happening in this question because, like I said, I really don’t understand it at this point. I’ve been in this situation a thousand times before though and am confident that as I keep working through this unit, at some point the ‘Divergence Test’ will start to make sense to me.

I’m now 20% of the way through Series (400/2,000 M.P.) but, since completing all the exercises only gets you 80% of the way through the M.P. and the unit test accounts for the final 20%, in a way I’m a quarter through this unit already! (Apart from the unit test.) That said, I still have 47 videos left to watch (are you kidding me?! 😳) and 15 exercises left to work through. With ~6 weeks left to go, I think it’’s a tall order’ll be tough to get this all done by the end of the year but that it’s still within reach!

It makes me think of that saying, “how do you eat an elephant? One bite at a time,” only in my case it’s more like, “how do you get through 47 videos? One video at a time.”