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1. Guys, I've been struggling with this question literally all day.
I would really, really, really appreciate if anyone could explain how to solve it using binomial expansion!

So here it is:
When (1- 3/2x)^p is expanded in ascending powers of x, the coefficient of x is -24.

a) find the value of p
b) find the coefficient of x^2
c) find the coefficient of x^3
2. (Original post by majdalemon)
Guys, I've been struggling with this question literally all day.
I would really, really, really appreciate if anyone could explain how to solve it using binomial expansion!

So here it is:
When (1- 3/2x)^p is expanded in ascending powers of x, the coefficient of x is -24.

a) find the value of p
b) find the coefficient of x^2
c) find the coefficient of x^3

So you know about the nCr button on your calculator (related to Pascal's number)?

You know that the coefficient of x will be the (nCr value)*(-³/2x). The 1 can be ignored since it's always going to be one to any power.

So let's call the nCr value N.

N*(-³/2)=-24

So N=16

This means for a) p=16 because the first coefficient is always the same as the power it's too. 3C1 gives 3 for example.
3. (Original post by majdalemon)
Guys, I've been struggling with this question literally all day.
I would really, really, really appreciate if anyone could explain how to solve it using binomial expansion!

So here it is:
When (1- 3/2x)^p is expanded in ascending powers of x, the coefficient of x is -24.

a) find the value of p
b) find the coefficient of x^2
c) find the coefficient of x^3
For b)

Since you know p=16 do 16C2*(-3/2)² which is 270.

c) 16C3*(-3/2)³=1890

Does this make sense? Please ask me to clarify things or explain why since I don't know how you've learnt it so far!
4. It's easier just to expand using the binomial theorem .. and then compare coefficients.
5. (Original post by hippoposthumous)
For b)

Since you know p=16 do 16C2*(-3/2)² which is 270.

c) 16C3*(-3/2)³=1890

Does this make sense? Please ask me to clarify things or explain why since I don't know how you've learnt it so far!

THANK YOU SOOSOSOOSSOOSOSOSOSOS MUCH!! You are AMAZING! Thank you!!!!!!!!!!!
6. (Original post by majdalemon)
THANK YOU SOOSOSOOSSOOSOSOSOSOS MUCH!! You are AMAZING! Thank you!!!!!!!!!!!

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Updated: January 24, 2015
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