Binomial Expansions Q

a) find the binomial expansion of (1+kx)^-2 up to and including the term x^3 where k is a constant

b) the binomial expansion in ascending powers of x of (1+kx)^-2 - (1+x)^n is 6x^2 + px^3 +...
(i) show that n= -2k
(ii) given n<0, find the value of p

I have put the x^3 expansions for both together to create:
(-4k^3) - ((n^3)-(3n^2)+(2n))/6 = p <---- I divided by x^3 to get rid of them

If I sub n=-2k then factorise to get solutions of k I get:
k=0 k=-1/4 k=1

If I then sub this into n=-2k I get:
n=0 n=1/2 n=-2

Then I assumed n=-2 because n<0

If I have done that correct, what do I do with n or k?
If I haven't done that correct, what am I supposed to do?

Reply 1

TeeEm

19

Original post by shuayb96

a) find the binomial expansion of (1+kx)^-2 up to and including the term x^3 where k is a constant

b) the binomial expansion in ascending powers of x of (1+kx)^-2 - (1+x)^n is 6x^2 + px^3 +...
(i) show that n= -2k
(ii) given n<0, find the value of p

I have put the x^3 expansions for both together to create:
(-4k^3) - ((n^3)-(3n^2)+(2n))/6 = p <---- I divided by x^3 to get rid of them

If I sub n=-2k then factorise to get solutions of k I get:
k=0 k=-1/4 k=1

If I then sub this into n=-2k I get:
n=0 n=1/2 n=-2

Then I assumed n=-2 because n<0

If I have done that correct, what do I do with n or k?
If I haven't done that correct, what am I supposed to do?

It might be easier if you post a .photo of the question and your workings.

Reply 2

davros

16

Original post by shuayb96

a) find the binomial expansion of (1+kx)^-2 up to and including the term x^3 where k is a constant

b) the binomial expansion in ascending powers of x of (1+kx)^-2 - (1+x)^n is 6x^2 + px^3 +...
(i) show that n= -2k
(ii) given n<0, find the value of p

I have put the x^3 expansions for both together to create:
(-4k^3) - ((n^3)-(3n^2)+(2n))/6 = p <---- I divided by x^3 to get rid of them

If I sub n=-2k then factorise to get solutions of k I get:
k=0 k=-1/4 k=1

If I then sub this into n=-2k I get:
n=0 n=1/2 n=-2

Then I assumed n=-2 because n<0

If I have done that correct, what do I do with n or k?
If I haven't done that correct, what am I supposed to do?

You can't "sub n =-2k" because you're supposed to be proving that n = -2k!!!

Just write out the first few terms of each binomial expansion and subtract one from the other. Compare the coefficients of what's left with the expansion they have given you.

Reply 3

shuayb96

OP

Original post by davros

You can't "sub n =-2k" because you're supposed to be proving that n = -2k!!!

Just write out the first few terms of each binomial expansion and subtract one from the other. Compare the coefficients of what's left with the expansion they have given you.

I already proved that n=-2k in part (i)

I was just trying to use that in part(ii) to then calculate the value for 'p'

Reply 4

davros

16

Original post by shuayb96

I already proved that n=-2k in part (i)

I was just trying to use that in part(ii) to then calculate the value for 'p'

I can't quite follow what you've done for part(ii). Before you can calculate the value of p, you need to find the correct value of k (and hence n). You haven't used any information about the coefficient of x^2.