IGCSE/GCSE/O & A Level/IB/University Student Forum

Qualification => Subject Doubts => GCE AS & A2 Level => Math => Topic started by: T.Q on January 04, 2010, 07:19:00 pm

Title: C2 HEELP
Post by: T.Q on January 04, 2010, 07:19:00 pm

The first four terms, in ascending powers of x, of the binomial expansion of (1 + kx)^n are

1 + Ax + Bx2 + Bx3 + …,

where k is a positive constant and A, B and n are positive integers.

(a) By considering the coefficients of x2 and x3, show that 3 = (n – 2) k.    (4 MARKS)

Given that A = 4,

(b) find the value of n and the value of k.     (4 MARKS)



PLZ SHOW YOUR WORKING

Title: Re: C2 HEELP
Post by: T.Q on January 06, 2010, 09:46:23 am

heeeeeeeeeelp
heeeeeeeeeelp
heeeeeeeeeelp        ???

Title: Re: C2 HEELP
Post by: astarmathsandphysics on January 06, 2010, 10:25:49 am

trythis.

Title: Re: C2 HEELP
Post by: XFlufferzX on January 06, 2010, 07:13:06 pm

Incase if my handwriting wasnt clear there ya go :
Using the identity:
(1+kx)^n = 

1 + n (kx) + n (kx) + n(n-1)/2! k^2 + n(n-1)(n-2)/3! kx^3

1+ Ax + Bx^2 + Bx^3

so A = nk
    B=  n(n-1)/2! k^2
    B= n(n-1)(n-2)/3! k^3

(2!= 2 , 3! =6)

Equating the problem:

n(n-1)/2 k^2 = n(n-1)(n-2)/6 k^3

Simplify it and you'll get

3= (n-2) k

For b)

3 = (n-2) k
Simplify

3 = nk -2k

3 = A -2k

3 = 4 - 2k

K = 1/2

Solving for n

A = nk

4 = n(0.5)

n=8

Its a good question, from which paper did you get dat?

Title: Re: C2 HEELP
Post by: T.Q on January 06, 2010, 09:02:39 pm

thank you both

its from the mock paper

Title: Re: C2 HEELP
Post by: T.Q on January 06, 2010, 09:32:13 pm

Quote from: XFlufferzX on January 06, 2010, 07:13:06 pm

Incase if my handwriting wasnt clear there ya go :
Using the identity:
(1+kx)^n = 

1 + n (kx) + n (kx) + n(n-1)/2! k^2 + n(n-1)(n-2)/3! kx^3

1+ Ax + Bx^2 + Bx^3

so A = nk
    B=  n(n-1)/2! k^2
    B= n(n-1)(n-2)/3! k^3

(2!= 2 , 3! =6)

Equating the problem:

n(n-1)/2 k^2 = n(n-1)(n-2)/6 k^3

Simplify it and you'll get

3= (n-2) k

For b)

3 = (n-2) k
Simplify

3 = nk -2k

3 = A -2k

3 = 4 - 2k

K = 1/2

Solving for n

A = nk

4 = n(0.5)

n=8

Its a good question, from which paper did you get dat?

the paper is attached

Title: Re: C2 HEELP
Post by: XFlufferzX on January 07, 2010, 09:34:50 am

thanks!  :D