Binomial Expansion Question

kalyan601

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Apr 27, 2014
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Hi, how would I start this question?

Given that the expansion of (1+cx)n begins 1+24x+264x2….. find c and n.

I'm really not sure how to begin. I can do questions asking me to expand the bracket, but I don't really know how to do it the other way around. I normally find the coefficients by using the nCr button on my calculator or pascals triangle for the small ones.


Thanks for your help in advance!
 
Hi, how would I start this question?

Given that the expansion of (1+cx)n begins 1+24x+264x2….. find c and n.

I'm really not sure how to begin. I can do questions asking me to expand the bracket, but I don't really know how to do it the other way around. I normally find the coefficients by using the nCr button on my calculator or pascals triangle for the small ones.


Thanks for your help in advance!

First, expand (1+cx)n in terms of 'c' and 'n' and 'x'.
 
When you say "I can do questions asking me to expand the bracket", do you mean for powers like 2 or 3 or do you know how to do it for general "n"?

The "binomial theorem" says that \(\displaystyle (a+ b)^n= \sum_{i= 0}^n \begin{pmatrix}n \\ i \end{pmatrix} a^{n-i}b^i\) so the first few terms are
\(\displaystyle (a+ b)^n= a^n+ na^{n-1}b+ \frac{n(n- 1)}{2}a^{n- 2}b^2+ \cdot\cdot\cdot\).

In this problem, a= 1 and b= cx.
 
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