HL Maths- mclaurins/ratio test

muffinz

Right so, im uber confused over the whole mclaurens series!

They tell you to get the first 4 terms of mclaurins, so you do fx, then f0, then f'x and f'o etc and then you sub it into the equation yes?

and then it tells you to get the general term or w.e its called, and this is where im verrrry confused!

my grinds teacher told me that :
x^2n-1 over (2n-1)! by(-1)^n+1 is for odd terms
and
x^2n-2 over (2n-1)! by (-1)^n+1 is for even terms

i got it at the time but now im so confused coz im looking at the exam papers and theyre getting totally different things.. can someone help me?! pretend your teaching it to a 5 yr old, dont get too techinical :P

thanks!!

Ashashi

Currently in the same boat, it is very confusing. I got it at the time in class, but just can't get it now.

Some help would be appreciated

EuropeanSon

General term I can't really help you with, I sort of intuitively figure them out myself, without a formula/method. You are correct about maclaurin, the 4th term would be (f'''0)x^3/3! and so on.

zam

It's pretty hard to explain especially over typing! But basically:
1. Just look at the series and try to use your common sense. Remember GENERAL term so it has to fit all of them
2. If it's only even numbers, put (x to the power of 2n) over (2n)!
3. If it's odds, put (x to the power of 3n) over (3n)!
4. If it's both, x to the power of n over n!
5. If the terms alternate between - and +, multiply your general term by (-1) to the power of n

**Timbuk2**

Guys, just use the sum to n terms of APs and GPs to figure out the general term. You will have the answer in about 2 lines, fully right. Just make sure to add in either (-1)^n or (-1)^n-1 depending on whether each odd or even term has a minus sign.

muffinz

zam wrote: »

It's pretty hard to explain especially over typing! But basically:
1. Just look at the series and try to use your common sense. Remember GENERAL term so it has to fit all of them
2. If it's only even numbers, put (x to the power of 2n) over (2n)!
3. If it's odds, put (x to the power of 3n) over (3n)!
4. If it's both, x to the power of n over n!
5. If the terms alternate between - and +, multiply your general term by (-1) to the power of n

so is what i have written above at all right? do i just have to manipulate it? i still dont really get how i do that or even why

dynamot

**Timbuk2** wrote: »

Guys, just use the sum to n terms of APs and GPs to figure out the general term. You will have the answer in about 2 lines, fully right. Just make sure to add in either (-1)^n or (-1)^n-1 depending on whether each odd or even term has a minus sign.

if the -1 ^ n+1 etc confuses you, just forget about it. Simply put whatever you are testing for convergence in absolute brackets, that is perfectly acceptable

H2student

You could try to figure out how to write the general term & how to do the test for them. I've spent hours 2-3 months ago trying to figure it out. I still can't do them and then I realised that the test is worth 5 marks. Learning how to expand the series is definitely worth learning though as it's easy and worth a lot of marks.

muffinz

H2student wrote: »

You could try to figure out how to write the general term & how to do the test for them. I've spent hours 2-3 months ago trying to figure it out. I still can't do them and then I realised that the test is worth 5 marks. Learning how to expand the series is definitely worth learning though as it's easy and worth a lot of marks.

is explanding the series the whole fx, f0, f'x, f'0?? im so confused!!

and for each series theres a general term yeah? im just going to learn them off by heart tonight!! if they ask for the general term, you just regurgitate it back to them dont you, theres no way to show how you got it is there?

zoom!

If you don't get the general term right and do the coreect procedure for ratio test you lose very little marks

JerCotter7

1. The powers and coefficients of each series are in an arithmetic series. Use
the formula for the general term of an arithmetic series Tn to generate Un .

2. Sometimes the signs alternate: +, −, +, −, +, −....... Multiply by (−1)^n−1
to achieve this alternation.

1, 2, 3,..... [Arithmetic series a = 1, d = 1]

Tn = a + (n-1)d

Tn = 1 + (n-1)1

Tn = n

x^n/n

And since if it alternates put multiply (-1)^n-1. Or change it to n depending on if you count n or n+1 as the first term.
________________________________________

Not sure if that helps any bit.

muffinz

zoom! wrote: »

If you don't get the general term right and do the coreect procedure for ratio test you lose very little marks

thanks im so terrified about q8, i hate the way we have no choice

Tony1130

I could never learn Mcclaurin series was just too difficult for me :[ thts y im doin Q 9 on further probability in more detail but i will glance over mcclaurin . q9 can be the easiest on the paper or a difficult Q .. hopefully its one of the easier ones