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Quick Q on The binomial expansion. watch

1. Hi guys, just come across something in the Core Mathematics 2 textbook that I'm a bit stuck on (page 84, q6) <-- just incase I write it out horribly

I've managed to solve this question with a little nudge in the right direction but I was wondering if there was a different, slightly quicker method to solving it. Here's the question;

The coefficient of in the binomial expansion of , where n is a positive integer, is 7. Find the value of n.

Okay, so I figured that the coefficient of , which is 7, is equal to . From that I get 28, and that's where I got stuck. Someone told me that I know the answer is 8 because 28 is in the expansion of , but surely there's a quicker way than sitting there writing out pascal's triangle all the way to 8?!

Any help is greatly appreciated as usual :P
2. how did you get n/4
3. (Original post by lebron_23)
Hi guys, just come across something in the Core Mathematics 2 textbook that I'm a bit stuck on (page 84, q6) <-- just incase I write it out horribly

I've managed to solve this question with a little nudge in the right direction but I was wondering if there was a different, slightly quicker method to solving it. Here's the question;

The coefficient of in the binomial expansion of , where n is a positive integer, is 7. Find the value of n.

Okay, so I figured that the coefficient of , which is 7, is equal to . From that I get 28, and that's where I got stuck. Someone told me that I know the answer is 8 because 28 is in the expansion of , but surely there's a quicker way than sitting there writing out pascal's triangle all the way to 8?!

Any help is greatly appreciated as usual :P
Well:

(1 + x/2)^n

1 + nx + n(n-1)/2! (x/2)^2 +...

So:

[n(n-1)/2!]/4 = 7/4
4. Ignore my post actually.

I'm blabbering.
5. (Original post by TenOfThem)
how did you get n/4
Well, I used the binomial expansion as you normally would but with the power as n rather than a number. So the expansion in ascending order of x gave me x x . Then, making 7 = I got 28 as my answer. If I went wrong somewhere, please point it out and please feel free to give me tonnes and tonnes of help

Thanks
6. (Original post by lebron_23)
Well, I used the binomial expansion as you normally would but with the power as n rather than a number. So the expansion in ascending order of x gave me x x . Then, making 7 = I got 28 as my answer. If I went wrong somewhere, please point it out and please feel free to give me tonnes and tonnes of help

Thanks
You have not used the binomial expansion at all

7. (Original post by TenOfThem)
You have not used the binomial expansion at all

Oh, that's a bit of a problem then . I thought it was possible to use the nCr function to find the coefficients of the terms in the expansion? That's sort of how I got to my answer.. It seems to work, but please explain your method, it seems more expansion-ish. Thanks again lol..
8. (Original post by TenOfThem)
You have not used the binomial expansion at all

That's what I tried to type up!
9. (Original post by L'Evil Fish)
That's what I tried to type up!
Haha its cool, I understood. What I didn't understand was what I said in my above post meh
10. (Original post by lebron_23)
Oh, that's a bit of a problem then . I thought it was possible to use the nCr function to find the coefficients of the terms in the expansion? That's sort of how I got to my answer.. It seems to work, but please explain your method, it seems more expansion-ish. Thanks again lol..
I have used nCr but in the simplified version that you should have also been taught

You seemed to decide that nC2 = 1... why?
11. (Original post by TenOfThem)
I have used nCr but in the simplified version that you should have also been taught

You seemed to decide that nC2 = 1... why?
I didn't intend to make is equal 1. I thought that nC2 was equal to 28, because that divided by 4 would give the coefficient of .
12. 7 = I got 28 as my answer.
nC2 = 28

so, rewrite this using the formula to convert from nCr into factorials:

n! / (n-2)!2! = 28

then you can sort this out by removing the factorials and you should get a quadratic
13. (Original post by lebron_23)
I didn't intend to make is equal 1. I thought that nC2 was equal to 28, because that divided by 4 would give the coefficient of .
It is
14. (Original post by TenOfThem)
It is
Okay, that makes me feel much better, thank you. But now the problem is, I'm not sure how to get from nC2 = 28 to what n is equal to. I figured it was 8 because 28 is in pascal's triangle under the expansion of

Oh god, scrap all of that - I just realised how to get from nC2 = 28 to n = 8. Thank you for your help and patience though!!
15. (Original post by lebron_23)
Okay, that makes me feel much better, thank you. But now the problem is, I'm not sure how to get from nC2 = 28 to what n is equal to. I figured it was 8 because 28 is in pascal's triangle under the expansion of
By using the fact that
16. (Original post by lebron_23)

Oh god, scrap all of that - I just realised what I was doing wrong. Thank you for your help and patience though!!
ok
17. (Original post by Lunch_Box)
nC2 = 28

so, rewrite this using the formula to convert from nCr into factorials:

n! / (n-2)!2! = 28

then you can sort this out by removing the factorials and you should get a quadratic
Thank you SO much, I knew it wasn't as long and as difficult as I though it was - I just forgot about using the nCr to factorial equation *major facepalm*

Much appreciated!!
18. (Original post by TenOfThem)
By using the fact that
Haha the answer emerges.. Thanks a bunch again. This has been more informative than 99% of my lessons put together >.<

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