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C2 Binomial expansion mixed exercise

Okay so I was wondering if anyone can help me with this question, its in the Edexcel C2 book, Mixed Exercise 5E question 10.

In the binomial expansion of (2k+x)n , where k is a constant and n is a positive integer, the coefficient of x2is equal to the coefficient of x3
a. Prove than n=6k+2

Now i know then that nC2 x (2k)n-2 = nC3 x (2k)n-3
But am not really sure what do do with this, can anyone help and explain what to do?
Thanks

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Original post by BenR17
Okay so I was wondering if anyone can help me with this question, its in the Edexcel C2 book, Mixed Exercise 5E question 10.

In the binomial expansion of (2k+x)n , where k is a constant and n is a positive integer, the coefficient of x2is equal to the coefficient of x3
a. Prove than n=6k+2

Now i know then that nC2 x (2k)n-2 = nC3 x (2k)n-3
But am not really sure what do do with this, can anyone help and explain what to do?
Thanks


Quick question...
Do you know what nC2 means?
Reply 2
Avatar for TenOfThem
TenOfThem
18
Original post by m4ths/maths247
Quick question...
Do you know what nC2 means?


prsom

just what I was about to ask
Original post by m4ths/maths247
Quick question...
Do you know what nC2 means?


Yeah, otherwise i wouldnt of got to question 10:biggrin:
Reply 4
Avatar for TenOfThem
TenOfThem
18
Original post by BenR17
Yeah, otherwise i wouldnt of got to question 10:biggrin:


Then write them in full

Do lots of cancelling

And there is your answering
Original post by TenOfThem
Then write them in full

Do lots of cancelling

And there is your answering


What do you mean by full?
Original post by BenR17
Yeah, otherwise i wouldnt of got to question 10:biggrin:


ergo you should find the question relatively straight forward :smile:
Reply 7
Avatar for TenOfThem
TenOfThem
18
Original post by BenR17
What do you mean by full?


Hence the question "do you know what they actually mean"


Can you explain what you think nCr means
(edited 10 years ago)
Original post by m4ths/maths247
ergo you should find the question relatively straight forward :smile:


I know that nC​2 it means n row of pascals triangle, choose the 2nd number
Original post by BenR17
I know that nC​2 it means n row of pascals triangle, choose the 2nd number


No, the other formula. The one that doesn't need the triangle.

I think what they are asking is whether you know what nCr actually represents?

Posted from TSR Mobile
Original post by BenR17
I know that nC​2 it means n row of pascals triangle, choose the 2nd number


So you do not know what it means

Have you ever seen it shown as factorials
Original post by majmuh24
No, the other formula. The one that doesn't need the triangle.

I think what they are asking is whether you know what nCr actually represents?

Posted from TSR Mobile


Other formula?
Original post by BenR17
Other formula?


Do you know a formula for nCr or do you just use the triangle?

Posted from TSR Mobile
Original post by BenR17
Other formula?


With the factorials
Original post by majmuh24
Do you know a formula for nCr or do you just use the triangle?

Posted from TSR Mobile


I just use the calculator and do like 6C3 for instance, thats all ive been taught
Original post by BenR17
I just use the calculator and do like 6C3 for instance, thats all ive been taught


Well then, you need to learn the formula.

nCr=n!r!(n−r)!=n×(n−1)×(n−2)⋯×(n−r+1)r!^n C _r = \dfrac{n!}{r!(n-r)!} = \dfrac{n \times (n-1) \times (n-2) \cdots \times (n-r+1)}{r!}

Posted from TSR Mobile
Original post by BenR17
I just use the calculator and do like 6C3 for instance, thats all ive been taught


You will struggle to do this question without understanding how nCr works

I suggest that you look in your text book for examples
Original post by TenOfThem
You will struggle to do this question without understanding how nCr works

I suggest that you look in your text book for examples


I have been looking through the text book, there arnt any examples of questions like that, between the text book and my teacher for binomial theyre pretty useless
Original post by BenR17
I have been looking through the text book, there arnt any examples of questions like that, between the text book and my teacher for binomial theyre pretty useless


Check youtube for

nCr factorial

or

binomial expansion
Original post by majmuh24
Well then, you need to learn the formula.

nCr=n!r!(n−r)!=n×(n−1)×(n−2)⋯×(n−r+1)r!^n C _r = \dfrac{n!}{r!(n-r)!} = \dfrac{n \times (n-1) \times (n-2) \cdots \times (n-r+1)}{r!}

Posted from TSR Mobile


Thank you, I know that this isnt displayed in the text book like that, and it doesnt even speak about it or how to use it so i dont expect how they want us to answer questions with it:frown:

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