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# Using maclurin series to find sums to infinity? Watch

1. Hey, I'm trying to use the maclurin series for to try and find...

1)

2)

3)

I've found the maclurin series for is .

The question also hints to differentiate term-by-term twice, but I'm not seeing the relationship.
2. so you know how to calculate . Can you think of a suitable substitution to turn x^r into ?
If you differentiate term by term, what do you get? As a consequence, you know how to work out that sum as well.
3. ah ok, thanks, i knew I had to use x=1/3 for part i, because of the standard a/1-r formula. Just wasn't seeing the link.

Now for part ii do I have to use the fact that...

and also differentiating the geometric progression gives me ?
4. (Original post by DJB MASTER)
Now for part ii do I have to use the fact that...

I presume you mean the derivative of the LHS is the RHS?
?
Yes. You can then make a substitution to get part ii

For part iii you won't quite get r^2x^r, but you'll get something similar, so you can add something on to get r^2x^r.
5. yeh, i meant the derivativee, sry about that. I got part ii working ok.

I'm stuck on the final part of iii...

I say the 2nd derivative of...

I expand and subtract the summations...

Is my working correct? I can see that the middle term is my 2nd derivativee of the geometric progression (2/(1-x)^3) multiplied by x^2, where x = 1/3. It's the last summation term that has me confused.

Is this just simply the answer I got for ii?
6. (Original post by DJB MASTER)
yeh, i meant the derivativee, sry about that. I got part ii working ok.

I'm stuck on the final part of iii...

I say the 2nd derivative of...

I expand and subtract the summations...

Is my working correct? I can see that the middle term is my 2nd derivativee of the geometric progression (2/(1-x)^3) multiplied by x^2, where x = 1/3. It's the last summation term that has me confused.

Is this just simply the answer I got for ii?
Yes.
You may need to be careful with the starting index of the sums. You have it correct here, but . In order to get the other side, just add on a few numbers to the beginning (you know what is, right?)

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