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How would I expand this? :/

(1+x+x^2) ^1/2

The question says expand as a series so I assumed it means using the binomial expansion for fractional powers, I'v attempted it, but I know its wrong, and I may sound stupid, but I'v never used binomial when there is three terms in the bracket! Lol any help will be appriciated :biggrin:


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Reply 1
Avatar for TenOfThem
TenOfThem
18
You need to expand (1+y)^1/2

Then substitute (x+x^2) for y
Reply 2
Avatar for raheem94
raheem94
13
Original post by Aneesa.x
(1+x+x^2) ^1/2

The question says expand as a series so I assumed it means using the binomial expansion for fractional powers, I'v attempted it, but I know its wrong, and I may sound stupid, but I'v never used binomial when there is three terms in the bracket! Lol any help will be appriciated :biggrin:


This was posted from The Student Room's iPhone/iPad App


Expand [1+(x+x2)]12 [ 1 + (x+x^2)]^{\frac12}
Reply 3
Avatar for Alexx53
Alexx53
You just take (x+x^2) as 1 term.

So you get [1+(x+x^2)]^1/2
Reply 4
Avatar for Aneesa.x
Aneesa.x
OP
4
Original post by TenOfThem
You need to expand (1+y)^1/2

Then substitute (x+x^2) for y


That's what I done, I get the wrong answer :/

Could you show me some steps? Maybe I'v gone wrong in my working somewhere..



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Reply 5
Avatar for raheem94
raheem94
13
Original post by Aneesa.x
That's what I done, I get the wrong answer :/

Could you show me some steps? Maybe I'v gone wrong in my working somewhere..



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[1+(x+x2)]12=1+12(x+x2)+12(12−1)2!(x+x2)2+… \displaystyle [1+(x+x^2)]^{\frac12} = 1 + \frac12 (x+x^2) + \frac{\frac12 \left( \frac12 - 1 \right) }{2!} (x+x^2)^2 + \ldots
Reply 6
Avatar for Notnek
Notnek
21
Original post by Aneesa.x
That's what I done, I get the wrong answer :/

Could you show me some steps? Maybe I'v gone wrong in my working somewhere..

Post your working.
Reply 7
Avatar for Aneesa.x
Aneesa.x
OP
4
Oh wait I got it now :biggrin: lol .. silly mistake -___-

Thanks everyonee :biggrin:


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Reply 8
Avatar for violetheart
violetheart
I don't understand this at all, is it C2 level stuff?

Because in C2 you never do binomial to the power of a 1/2.

Can someone show me how you do a binomial expansion to the power of a 1/2 please? :smile:
(edited 11 years ago)
Reply 9
Avatar for TenOfThem
TenOfThem
18
Original post by violetheart
I don't understand this at all, is it C2 level stuff?

Because in C2 you never do stuff to the power of a 1/2.

Can someone show me how you do a binomial expansion to the power of a 1/2 please? :smile:


It is C3
Reply 10
Avatar for raheem94
raheem94
13
Original post by violetheart
I don't understand this at all, is it C2 level stuff?

Because in C2 you never do binomial to the power of a 1/2.

Can someone show me how you do a binomial expansion to the power of a 1/2 please? :smile:


Original post by TenOfThem
It is C3


In edexcel it is C4.
Reply 11
Avatar for Aneesa.x
Aneesa.x
OP
4
Original post by violetheart
I don't understand this at all, is it C2 level stuff?

Because in C2 you never do stuff to the power of a 1/2.

Can someone show me how you do a binomial expansion to the power of a 1/2 please? :smile:


There is a different formula for binomial expansions with fraction or negative powers, don't worry about it yet if you're doing C2 :smile:


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Original post by raheem94
In edexcel it is C4.


Maybe C4 then :smile:
Ahh, thankyou, I was pretty worried then :smile: I'm just starting C3 but I was wondering if I missed something important.

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