Binomial Expansion Question? Watch

iamabbie97
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#1
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Then we are told "Given that the third term of this series is 540x2

b) Show that k=6

c) Find the coefficient of x3"

Thing is, I did part a and didn't get 540x2 as the third term...

You don't need to give me the answer, if you feel that is me cheating, however I would kindly appreciate somebody pointing me in the right direction!

Thank you!
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Chlorophile
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(Original post by iamabbie97)

Then we are told "Given that the third term of this series is 540x2

b) Show that k=6

c) Find the coefficient of x3"

Thing is, I did part a and didn't get 540x2 as the third term...

You don't need to give me the answer, if you feel that is me cheating, however I would kindly appreciate somebody pointing me in the right direction!

Thank you!
What's your working?
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TeeEm
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(Original post by iamabbie97)

Then we are told "Given that the third term of this series is 540x2

b) Show that k=6

c) Find the coefficient of x3"

Thing is, I did part a and didn't get 540x2 as the third term...

You don't need to give me the answer, if you feel that is me cheating, however I would kindly appreciate somebody pointing me in the right direction!

Thank you!
your expansion in part (a) will be in terms of k

then you set that to 540(x2)
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iamabbie97
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(Original post by Chlorophile)
What's your working?
Here's a picture, sorry if it isn't very clear...I used the nCr (a)n (b)0 +nCr (a)n-1 + (b)1....

Formula, and then went down and down, I'm not the best with fractions, that might be why

P.S if it looks like an S, it's a 5, if the workings aren't clear to read, let me know and I'll quickly rewrite them
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iamabbie97
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(Original post by Chlorophile)
What's your working?

Here's a far better photo, I'm not even sure what I've done to be honest!
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iamabbie97
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(Original post by TeeEm)
your expansion in part (a) will be in terms of k

then you set that to 540(x2)
I've uploaded a picture of my workings, I don't think I've done it right
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TeeEm
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(Original post by iamabbie97)
I've uploaded a picture of my workings, I don't think I've done it right
it look correct to me ..

I think you should look at my previous post.
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iamabbie97
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(Original post by TeeEm)
it look correct to me ..

I think you should look at my previous post.
So I would put what I've got as my third term equal to 540x2 and go from there?
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Chlorophile
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(Original post by iamabbie97)
Here's a far better photo, I'm not even sure what I've done to be honest!
That all looks right to me... What did you do next?

(Original post by iamabbie97)
So I would put what I've got as my third term equal to 540x2 and go from there?
Yes, you make (5/2)k^3=540
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TeeEm
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(Original post by iamabbie97)
So I would put what I've got as my third term equal to 540x2 and go from there?
yes

equate the x2 terms
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iamabbie97
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(Original post by Chlorophile)
That all looks right to me... What did you do next?
I'm not too sure how to multiple the fractions with the other numbers, for example would the second term be 5xk4 ​/2 ?
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Chlorophile
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(Original post by iamabbie97)
I'm not too sure how to multiple the fractions with the other numbers, for example would the second term be 5xk4 ​/2 ?
Yes, which is the same thing as saying 2.5k^4x. You just multiply.
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iamabbie97
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(Original post by Chlorophile)
Yes, which is the same thing as saying 2.5k^4x. You just multiply.

So is this line of workings correct? And would that be the final expansion?
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Chlorophile
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(Original post by iamabbie97)
So is this line of workings correct? And would that be the final expansion?
Yes that's right (although obviously there are also more terms and you can simplify the fourth term).
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iamabbie97
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(Original post by Chlorophile)
Yes that's right (although obviously there are also more terms and you can simplify the fourth term).
Can I simplify it by dividing the 10 and 8 by 2? And would I be able to do that to the third term as well?
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Chlorophile
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(Original post by iamabbie97)
Can I simplify it by dividing the 10 and 8 by 2? And would I be able to do that to the third term as well?
Well 10/4 = 5/2 and 10/8 = 5/4 so yes!
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iamabbie97
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(Original post by Chlorophile)
Well 10/4 = 5/2 and 10/8 = 5/4 so yes!

Thank you so much for your help!
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iamabbie97
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(Original post by Chlorophile)
Well 10/4 = 5/2 and 10/8 = 5/4 so yes!
How do I find the coefficient of x3​?
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Chlorophile
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(Original post by iamabbie97)
How do I find the coefficient of x3​?
Well you know what k is so it's just a matter of subbing it in to the expression you've already got. The coefficient is the constant you're multiplying the x^3 by.
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davros
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(Original post by iamabbie97)
How do I find the coefficient of x3​?
Are you happy that you have shown that k = 6?

Just put k = 6 into your expansion and simplify the x^3 term to cancel any fractions etc.
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