Don't mess with mathematics!!
I'm not complaining or clan contempt, I just can't stand of my math lecturer anymore!! Today, mathematics lecturer class, our lecturer gave us a few revision questions to do. Then come to question number 3...
Find the nth term in following geometric progression.
3, 1, 1/3, ...
Show that the G.P is convergent or divergent.
Find the sum to infinity.
* I wrote the question based on my memory... So it maybe a bit different from the actual.
The first part I don't think need to explain... Because what I want to talk about is part 2.
Before I move on, let me explain how she solved the question. At first, she tell us the that the sequence is convergent. Suddenly, a student asked, why it is convergent. Funny, she stunned and turn to the white board and tried to solve the prove it secretly... She writing all the lim (n approach infinity)... She refer to notes... Then come out with result that the sequence is divergent... Then is my turn to stunned!
Well, based on our previous lecturer, he told that when the sequence is getting smaller and smaller, at the end it will stop at 0 or any other number. Therefore, the sequence is convergent. Divergent is when the sequence getting larger and larger and it will not stop on a specific number but keep on growing.
Ok, back to the question, the sequence is, obviously, decreasing. So, its definitely that this sequence is convergent. I told her the same thing (I even bring our previous lecturer into my answer!). What she reply? Gosh... she said it is explanation and looked like she is not accepted it.
Then I said, if the sequence is divergent, we can't even find the sum to infinity, but we had found it! It proved that the sequence is convergent! Then she answer me that is the matter of the order of question...
Fine! Then we stick to her method. The nth term is =3(1/3)n-1
So, when ...
Limn->∞ 3(1/3)n-1 = 3 . Limn->∞ (1/3)n-1
Which Limn->∞ (1/3)n-1 = 0
Then anything times with 0 equals to 0. In other word, the sequence will stop at 0 somehow. Therefore, the sequence is so not a divergent!
Some may asked, why Limn->∞ (1/3)n-1 = 0
Well, 1/3 and (1/3)2 ,which is smaller? Obviously, is (1/3)2
Then when the n(the power) keep on growing, the number will get more closer to 0 and finally stop at 0. Therefore, Limn->∞ (1/3)n-1 = 0
Actually, I feel so guilty after the class... I mean, I used a very rude tone when I talk(well, it looked more like argue...) with her... I'm so sorry... I just can't control my temper... This is not the first time I get angry and louder my voice to other people... I don't know why my temper can be so... bad... I promise, I will change it... I force myself to...
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