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A2 C4 Maths help - Binomial expansion question

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1. I've been going through the 2015 C4 maths paper and cannot figure out how you do the second part to this question:
Find the binomial expansion of up to and including the term in . [3 marks]

I think the answer to this is: 1/4 - x/16 +( 5x^2)/256

(ii) Use your expansion from part (b)(i) to find an estimate for , giving your answer to four decimal places. [2 marks]

Any help on (ii) would be really appreciated!
Thank you.
2. (Original post by EmJ15)
I've been going through the 2015 C4 maths paper and cannot figure out how you do the second part to this question:
Find the binomial expansion of up to and including the term in . [3 marks]

I think the answer to this is: 1/4 - x/16 +( 5x^2)/256

(ii) Use your expansion from part (b)(i) to find an estimate for , giving your answer to four decimal places. [2 marks]

Any help on (ii) would be really appreciated!
Thank you.
what you do is use trial and improvement and try and make your become , by playing around with the first equation once that x value gives you the second equation what you do is sub in that value of x into your expansion and find the value
3. So the expansion is valid for . What happens if you let x=1/3.
4. (Original post by EmJ15)
I've been going through the 2015 C4 maths paper and cannot figure out how you do the second part to this question:
Find the binomial expansion of up to and including the term in . [3 marks]

I think the answer to this is: 1/4 - x/16 +( 5x^2)/256
This bit is correct.

(ii) Use your expansion from part (b)(i) to find an estimate for , giving your answer to four decimal places. [2 marks]

Any help on (ii) would be really appreciated!
Thank you.
If you notice that:

Then it is fairly obvious that gives you and you can plug this into your binomial expansion to get an approximation.
5. (Original post by Zacken)
This bit is correct.

If you notice that:

Then it is fairly obvious that gives you and you can plug this into your binomial expansion to get an approximation.
Thank you! That makes more sense now.
6. (Original post by EmJ15)
Thank you! That makes more sense now.
You're welcome!

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