## Friday, 16 September 2011

### TMA06 M208 Back

Well got the 6th TMA for M208 back not bad in the 90's but the elusive 100% escapes me it highlighted one point which I had totally missed. Also it just goes to show how counterintuitive analysis can be.

The series

$$\sum_{0}^{\infty}\frac{1}{n}$$  is divergent but the sum

$$\sum_{0}^{\infty}\frac{-1^n}{n}$$ is convergent

to some people on the forums this seems obvious but to me given that the second series has alternating terms I would think it diverges to two different series. Anyway at least I know now.

Started revising my plan is to do 1 paper per week per course under exam conditions at the start of each weekend and then to consolidate my answers revise topics I'm not sure about until, the last few days before the exams. Which I will take off and try and do two papers for each course on the last four days. That will make a total of five past papers per course which should be enought. At least the exams are on the same day so I can divide my time equally on each course before each exam.

Anyway I'll review Richard 2nd later on this weekend and also summarise the first section of Hume's Enquiry.

1. Good work on the TMA Chris. 90+ is a cracking score.

Best regards

Dan

2. ps: I'm not sure the second series would alternate in sign. Wouldn't it just start at -1 and then converge on zero?

I'd be interested to know, if you have the text answer

Ta
Dan

3. The second series does have alternating terms and both converge to different limits.

But the sum of two series with two different limits is equal to the sum of the two limits.

So the original does converge to a definite limit. Wish I knew what it was!

4. I dropped 2 marks on TMA06 (among others dropped) , by copying and pasting a textbook answer(altering a 5 to a 7).

Very annoying when the textbook answers lose marks, as the way the textbook did it was 'not on the mark scheme'.

5. 'The second series does have alternating terms and both converge to different limits.'

Actually, I now think this is rubbish. A series can be made up of two subsequences which both diverge and yet the series can converge.

One example is 1 -1 + 1/2 - 1/2 + 1/3 - 1/3 etc.

6. Hi Cheers Steve thanks for your comments I think to some extent you just have to learn these things off by heart and then the underlying logic will reveal itself. A bit like learning chess openings or end games.
For example I think I can just about understand the logic behind epsilon delta defintions of continuity and I even managed to get the gist ofthe continuity of the blancmange function but ask me to do these unaided and I would probably fall at the first hurdle.