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Series and sequences question

I dunno what to do i would be gratefull if someone was to help me. Thanks

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.

Given that A = 4,
(b) find the value of n and the value of k.

if anyone has got a marksheme for mock paper edexcel C2
it would be great
Reply 1
Avatar for dvs
dvs
10
Instead of posting the same thread a couple of times, maybe you could tell us what ideas you have? :wink:

Using the binomial theorem, what does the coefficient of x^2 look like? And x^3? Notice that they're both B, so they're equal.

And what does the coefficient of A look like? You know that this equals 4, and you have the equation from part (a). So solving a couple of equations simultaneously doesn't seem too far-fetched.
Reply 2
Avatar for Jonny W
Jonny W
8
Coefficient of x^2 = (1/2)n(n - 1)k^2
Coefficient of x^3 = (1/6)n(n - 1)(n - 2)k^3

Since those two coefficients are equal,

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

(b)
nk = 4

Putting that into 3 = (n - 2)k gives 3 = 4 - 2k and k = 1/2. So n = 8.
Reply 3
Avatar for Rajeshshaym
Rajeshshaym
OP
2
sorry for posting it twice i didnt no how to dit.... i do now ....sorry

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