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:
But unfortunately I'm stuck with the verification of n=1/2.
Binomial expansion - MathMate, Wednesday, February 29, 2012 at 10:04am
The binomial expansion is usually expressed as:
[note: (n,r)=(n,n-r), so (n,n-2)=(n,2)]
so term n-2 is
and the coefficient
[n(n-1)/2!]*[4^(n-2)]* = -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.