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Binomial expansion (1+x)^n

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Binomial expansion (1+x)^n [#permalink] New post 05 Nov 2012, 06:33
Is there a shortcut to calculate (1+x)^n, where n is greater than or equal 4, apart from binomial expansion? It seems calculating using binomial expansion takes enough time that cannot be accommodated under GMAT constraints. So far, I have seen the use of such terms in calculation of compound interest, though of course they are not absolutely necessary. But it's always useful to be armed when going to war, ain't it?
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Re: Binomial expansion (1+x)^n [#permalink] New post 05 Nov 2012, 06:43
The only other method I know is Pascal's triangle.

http://en.wikipedia.org/wiki/Pascal's_triangle

If you do some practice, upto 10 should not be any prob.
But GMAT questions wont ask this. Everything is solvable within 2 mins.
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Re: Binomial expansion (1+x)^n [#permalink] New post 05 Nov 2012, 09:04
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ConnectTheDots wrote:
The only other method I know is Pascal's triangle.

http://en.wikipedia.org/wiki/Pascal's_triangle

If you do some practice, upto 10 should not be any prob.
But GMAT questions wont ask this. Everything is solvable within 2 mins.


I guess I should memorize the coefficients just in case. Thank you.
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Re: Binomial expansion (1+x)^n [#permalink] New post 21 Nov 2013, 18:06
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Re: Binomial expansion (1+x)^n [#permalink] New post 21 Nov 2013, 21:57
There is no need to learn the binomial expansion of (1+x)^n as far as the GMAT is concerned. You will not be tested on this concept. If they do test this concept, which so far they have not, they will give you the expression for the binomial expansion. If however, you do see a term such as (1+x)^18, then they are expecting you to manipulate the expressions without resorting to binomial expansion.

For example, on the GMAT they could ask the following question:

Given (1+x)^18=27, what is the value of (1+x)^12 ?

Take cube root of the equation (1+x)^18=27, which yields (1+x)^6=3, and then square this to yield (1=x)^12=9.

Such a question is fair game on the GMAT, in fact a similar idea has been tested on the exam.

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Re: Binomial expansion (1+x)^n [#permalink] New post 04 Dec 2013, 16:52
Expert's post
Hello all,
I agree that the GMAT will not expect folks to calculate the binomial expansions of high powers, but I still would recommend memorizing the basics of Pascal's triangle, because the numbers in Pascal's Triangle, the so-called "Binomial coefficients", are identical to the nCr numbers used in combinations. See:
http://magoosh.com/gmat/2012/gmat-math- ... binations/
Mike :-)
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Re: Binomial expansion (1+x)^n   [#permalink] 04 Dec 2013, 16:52
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