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# C2 Question watch

1. The coefficient of x2
in the binomial expansion of (1 + 0.4x)n
, where n is a positive integer, is 1.6

a Find the value of n.
b Use your value of n to find the coefficient of x
4
in the expansion.

need help on a, have no idea where to start,
thanks =)
2. Firstly, do you know how to work out the binomial expansion?
3. Expand as far as the term in

Set the coefficient of equal to 1.6.
4. Compare coefficient of the x^2 term
5. (Original post by Noble.)
Firstly, do you know how to work out the binomial expansion?
yes, using NcR notation.
6. (Original post by Hi, How are you ?)
yes, using NcR notation.
Ok, Mr. M has said how to proceed once you've done the binomial expansion up to the term.
7. (Original post by Mr M)
Expand as far as the term in

Set the coefficient of equal to 1.6.
Tried using NcR notation, and then I got
^ 1n + ^ 1n-1 ^ 0.4x + ^ 1n-2 ^ (0.4x)2
, What do i do next ?

8. So

You know that

You can use this to determine .
9. (Original post by Noble.)

So

You know that

You can use this to determine .
How would you get the n out of the brackets, what process would you do??
10. (Original post by Hi, How are you ?)
How would you get the n out of the brackets, what process would you do??

but the easiest way is just to write down a few rows of Pascal's triangle!
11. (Original post by Hi, How are you ?)
How would you get the n out of the brackets, what process would you do??
By definition
12. (Original post by Noble.)
By definition
so it means that

= n! / 2!(n-2)!
= n! / 2(n-2)!
13. (Original post by Hi, How are you ?)
so it means that

= n! / 2!(n-2)!
= n! / 2(n-2)!
Yep. Now note that n! = (n-1)(n-2)(n-3) x ... x 1 and (n-2)! = (n-2)(n-3)(n-4) x... x 1

So you should be able to see what terms cancel in the fraction.
14. (Original post by Noble.)
Yep. Now note that n! = (n-1)(n-2)(n-3) x ... x 1 and (n-2)! = (n-2)(n-3)(n-4) x... x 1

So you should be able to see what terms cancel in the fraction.
Flippin' heck. Isn't this all a bit OTT?

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1
15. (Original post by Mr M)
Flippin' heck. Isn't this all a bit OTT?

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1
Haha, you're right - although I do hate Pascal's triangle

Once you get familiarised with nCr though it obviously isn't anywhere near as cumbersome and you can just write

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