Binomial Expansions Q Watch

shuayb96
Badges: 0
Rep:
?
#1
Report Thread starter 4 years ago
#1
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?





0
reply
TeeEm
Badges: 19
Rep:
?
#2
Report 4 years ago
#2
(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.
0
reply
davros
  • Study Helper
Badges: 16
Rep:
?
#3
Report 4 years ago
#3
(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.
0
reply
shuayb96
Badges: 0
Rep:
?
#4
Report Thread starter 4 years ago
#4
(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'
0
reply
davros
  • Study Helper
Badges: 16
Rep:
?
#5
Report 4 years ago
#5
(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.
0
reply
Kevin De Bruyne
Badges: 21
Rep:
?
#6
Report 2 years ago
#6
(Original post by Sniperdon227)
ive got the answers
The OP is most likely done with their A-levels now
0
reply
Sniperdon227
Badges: 5
Rep:
?
#7
Report 2 years ago
#7
(Original post by SeanFM)
The OP is most likely done with their A-levels now
lol ive been on loads of threads for this q and no ones posted the answer
0
reply
Kevin De Bruyne
Badges: 21
Rep:
?
#8
Report 2 years ago
#8
(Original post by Sniperdon227)
lol ive been on loads of threads for this q and no ones posted the answer
Are you stuck with the method?
0
reply
RyJParker
Badges: 0
Rep:
?
#9
Report 2 years ago
#9
Hi, i am really stuck on the method for both parts (i)&(ii) in b, is anyone abke to come up with a solution?
0
reply
Notnek
  • Forum Helper
Badges: 20
Rep:
?
#10
Report 2 years ago
#10
(Original post by RyJParker)
Hi, i am really stuck on the method for both parts (i)&(ii) in b, is anyone abke to come up with a solution?
Can you please start a new thread and post the question along with your attempts?

If you post all your working then you're more likely to get help.
0
reply
RyJParker
Badges: 0
Rep:
?
#11
Report 2 years ago
#11
(Original post by notnek)
Can you please start a new thread and post the question along with your attempts?

If you post all your working then you're more likely to get help.

https://www.thestudentroom.co.uk/sho....php?t=4454708
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • Cranfield University
    Cranfield Forensic MSc Programme Open Day Postgraduate
    Thu, 25 Apr '19
  • University of the Arts London
    Open day: MA Footwear and MA Fashion Artefact Postgraduate
    Thu, 25 Apr '19
  • Cardiff Metropolitan University
    Undergraduate Open Day - Llandaff Campus Undergraduate
    Sat, 27 Apr '19

Have you registered to vote?

Yes! (499)
37.83%
No - but I will (101)
7.66%
No - I don't want to (90)
6.82%
No - I can't vote (<18, not in UK, etc) (629)
47.69%

Watched Threads

View All
Latest
My Feed