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C2 Binomial Expanison help

Hi, i have got an awnser to the below question part a, but im not sure if its right and i need help with part b.

In the binomial expansion, in ascending powers of x, of (1+ax)n, where a and n are constants, the coeffiecnt of x is 15. The coefficient of x2 and x3 are equal.

a) Find the value of a nad the value of n

b)find the coefficient of x3

any help is much appriciated
Reply 1
beccajonesy
Hi, i have got an awnser to the below question part a, but im not sure if its right and i need help with part b.

In the binomial expansion, in ascending powers of x, of (1+ax)n, where a and n are constants, the coeffiecnt of x is 15. The coefficient of x2 and x3 are equal.

a) Find the value of a nad the value of n

b)find the coefficient of x3

any help is much appriciated

So what was your answer for part a)? :smile:
Reply 2
i got a=6 and n=2.5 :s-smilie:
Reply 3
beccajonesy
i got a=6 and n=2.5 :s-smilie:

Me too. :yep:


So then you can do part b): find the coefficient of x3x^3 by applying the binomial expansion, substituting in those values. :yes:

Remember that when nn is not an integer, the binomial coefficients are defined without using n! (because n has to be an integer to get a factorial of it):
(nr)=n(n1)(n2)(nr+1)r!\displaystyle \binom{n}{r} = \frac{n(n-1)(n-2)\cdots(n-r + 1)}{r!}

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