Homework Help: Binomial expansion

Posted by Helga on Wednesday, February 29, 2012 at 8:41am.

The coefficient of x^2 in the expansion of (4-3x)^n as a series of ascending powers of x is -9/64. Show that n satisfies the equation 4^(n+1)=2/[n(1-n)] and hence verify that n=1/2.

I can do the first part of the problem:
4^n*3^2*n(n-1)/2!*2^4=-3^2/2^6
4*4^n*n(n-1)=-2
4^(n+1)*n(n-1)=-2
4^(n+1)=2/[n(1-n)]

But unfortunately I'm stuck with the verification of n=1/2.
Please help.

Binomial expansion - MathMate, Wednesday, February 29, 2012 at 10:04am
The binomial expansion is usually expressed as:
(p+q)^n
=∑ (n,r)p^i*q^(n-i)
for i=0,n
where (n,r)=n!/[r!(n-r)!]

so for
p=4
q=-3x
i=(n-2)
(n,r)=n*(n-1)/2!
[note: (n,r)=(n,n-r), so (n,n-2)=(n,2)]
so term n-2 is
[n(n-1)/2!]*[4^(n-2)]*[(-3x)^2]
=[n(n-1)/2!]*[4^(n-2)]*[9]x²
and the coefficient
[n(n-1)/2!]*[4^(n-2)]*[9] = -9/64
Solve for n by trying various values of n that gives -9/64 on the left-hand side.

I get n=1/2.

Answer this Question

Related Questions

binomial expansion - how do you expand the following as a series of ascending ...
same type of binomial theorem question - Question: Find the first 3 terms in the...
maths - Use binomial theorem to to expand squareroot of 4+x in ascending powers ...
Maths - Determine the coefficient of x^5 in the binomial expansion of (2-3x)^7?
Integrated Math 1 - What is the coefficient of the xy^2 term in the expansion of...
Pre Cal. - The expression 81p^4 + 108 p^3 r^3 + 54p^2 r^6 + 12 pr^9 + r^12 is ...
Math - ç 2x^3 + 3x^2 + x + 1 dx --------------------- -2x + 1 [2x^3...
Math - Use the Binomial Theorem to determine the coefficient of x^14 in the ...
Binomial Expansion - Write the 6th term of the expansion of (x^2-2y)^9 and ...
Calculus - This is going to be pretty hard to show as text since it would be ...

For Further Reading

First Name:
School Subject:
Answer: