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Mega A Level Maths Thread MK II

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Original post by L'Evil Fish
No.

Why is it whenever I get side tracked everyone wants to go back... But then when everyone else goes off track, I just look like a whining bitch?:colonhash:

Anyway... We'll stop with this.

Back to maths.

Ok:
leveil.PNG
Original post by reubenkinara
Ok:
leveil.PNG


Where is that from?
Original post by MathsNerd1
Where is that from?

AEA. It's just C3 knowledge :smile:
Here's a semi-interesting question (Slightly more difficult than standard A Level but still straightforward):

Prove that arctanx=1−13x3+15x5+...+(−1)r12r+1x2r+1+... arctanx = 1- \frac{1}{3}x^3+\frac{1}{5}x^5+...+(-1)^r\frac{1}{2r+1}x^{2r+1}+...

(LotF, resist the urge, we know that you know the answer. :tongue: )
Original post by reubenkinara
AEA. It's just C3 knowledge :smile:


That's where I thought I saw the question from but I just wanted to be sure :tongue: I think I'll redo this question before I head up as I've already done it once but I've forgotten the answer :-/
Original post by DJMayes
Here's a semi-interesting question (Slightly more difficult than standard A Level but still straightforward):

Prove that arctanx=1−13x3+15x5+...+(−1)r12r+1x2r+1+... arctanx = 1- \frac{1}{3}x^3+\frac{1}{5}x^5+...+(-1)^r\frac{1}{2r+1}x^{2r+1}+...

(LotF, resist the urge, we know that you know the answer. :tongue: )


Original post by MathsNerd1
That's where I thought I saw the question from but I just wanted to be sure :tongue: I think I'll redo this question before I head up as I've already done it once but I've forgotten the answer :-/

Perhaps you should attempt this too!
Original post by reubenkinara
Perhaps you should attempt this too!


Yeah, I'm not too sure how to even approach something like that :-/
Original post by L'Evil Fish
How can I spam my own thread? It's mine to do as I please.

It's fine when everyone else does it :rolleyes:

Anyway,

Arctan(x) proof question above. How do you even start with things like that?

I wish I knew. I look forward to someone posting a solution though :biggrin:.
It looks like a Taylor expansion which means that each term can be integrated and differentiated. Don't you notice that the given terms look like they've been integrated?
(edited 10 years ago)
Original post by Boy_wonder_95
What is 'spam'? I got warning points too :rolleyes:


Off topic discussion, or smiley/photo without text. It's ridiculous at times.

I don't get why we get STEP questions here, when there are STEP threads, is that not spam?

Any tips for S1? Topics include, probability, Poisson and Binomial Distribution, their approximations, probability density functions and the calculus involved in that
Original post by L'Evil Fish
Off topic discussion, or smiley/photo without text. It's ridiculous at times.

I don't get why we get STEP questions here, when there are STEP threads, is that not spam?

Any tips for S1? Topics include, probability, Poisson and Binomial Distribution, their approximations, probability density functions and the calculus involved in that

When do we get STEP Qs on here?
I must have been afk at the time :frown: I assume it's because during times when there's been low thread activity, i.e few to no Alevel Qs so out of convenience those doing STEP just stayed on here to chat about it as opposed to migrating to that thread :smile:.
Original post by DJMayes
Here's a semi-interesting question (Slightly more difficult than standard A Level but still straightforward):

Prove that arctanx=1−13x3+15x5+...+(−1)r12r+1x2r+1+... arctanx = 1- \frac{1}{3}x^3+\frac{1}{5}x^5+...+(-1)^r\frac{1}{2r+1}x^{2r+1}+...

(LotF, resist the urge, we know that you know the answer. :tongue: )


DJ, can you post the solution now and spoiler it, if someone else wants to give it a try. As for me I don't know where to start.
Original post by DJMayes
Here's a semi-interesting question (Slightly more difficult than standard A Level but still straightforward):

Prove that arctanx=1−13x3+15x5+...+(−1)r12r+1x2r+1+... arctanx = 1- \frac{1}{3}x^3+\frac{1}{5}x^5+...+(-1)^r\frac{1}{2r+1}x^{2r+1}+...

(LotF, resist the urge, we know that you know the answer. :tongue: )

Spoiler

(edited 10 years ago)
Original post by MAyman12
DJ, can you post the solution now and spoiler it, if someone else wants to give it a try. As for me I don't know where to start.


Well, Felix has posted a solution so it's there for anyone who wants to see it. Reuben has given some very good advice for tackling the problem though.
Original post by Felix Felicis

Spoiler



Did you just Differentiate then Integrate or something? Couldn't do that cause I haven't done C3/C4 though.
Original post by MAyman12
Did you just Differentiate then Integrate or something? Couldn't do that cause I haven't done C3/C4 though.

Binomial expansion for negative exponents - unlikely you've seen it if you haven't done C3/ 4 :biggrin:
Original post by Felix Felicis
Binomial expansion for negative exponents - unlikely you've seen it if you haven't done C3/ 4 :biggrin:


Just read what was on the website. So it's simply the same as the binomial expansion in C2 but instead of positive powers we use negative ones but since it decreases with every term, it's infinite?
Original post by MathsNerd1
That's where I thought I saw the question from but I just wanted to be sure :tongue: I think I'll redo this question before I head up as I've already done it once but I've forgotten the answer :-/

Have you fallen asleep?
Original post by MAyman12
Just read what was on the website. So it's simply the same as the binomial expansion in C2 but instead of positive powers we use negative ones but since it decreases with every term, it's infinite?

Yes, however you can only use the 1+nx1!+n(n−1)x22!+...1+\dfrac{nx}{1!}+\dfrac{n(n-1)x^2}{2!}+... one.
Original post by reubenkinara
Have you fallen asleep?


Change of plans, I'll do it first thing when I get up as my brain isn't functioning too well at this hour :tongue: I know that's a rubbish excuse but yeah, I'm tired :redface:


Posted from TSR Mobile
Original post by reubenkinara
Yes, however you can only use the 1+nx1!+n(n−1)x22!+...1+\dfrac{nx}{1!}+\dfrac{n(n-1)x^2}{2!}+... one.


Why is that?:redface:

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