hey, ive got a question here in which ive been pondering over for hours, hope someone could help me ^^

If the coefficients of and in the expansion of are equal, find K.

thanks in advance =D

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- Feb 17th 2009, 01:03 AMteddybear67[SOLVED] binomial theorem =(
hey, ive got a question here in which ive been pondering over for hours, hope someone could help me ^^

If the coefficients of and in the expansion of are equal, find K.

thanks in advance =D - Feb 17th 2009, 01:48 AMADARSH
- Feb 17th 2009, 03:18 AMteddybear67
yea, thats where i got lost.

btw sorry the 10 is supposed to be 19, so its

i dont think it would make any difference in the working u gave me anyways. lols

anywyas, my working is

=

and i got stuck here... - Feb 17th 2009, 03:54 AMPlato
- Feb 17th 2009, 03:58 AMteddybear67
i dont get it...

i know what is

buthow did u get 9 and 10? - Feb 17th 2009, 04:15 AMmathaddict
don mean to post .

- Feb 17th 2009, 05:07 AMGrandadBinomial Coefficients
- Feb 17th 2009, 05:37 AMteddybear67
thanks alot grandad, but i dont get this part :

sorry, im confused over the factorial and the "choose". its the 1 part of binomial theorem in which i never get ><

oh ya, and the answer at the back of the book in which i got the question from is 11 and not 7. Do you know why? or is the book wrong? because there are times in which the book gives wrong answers... - Feb 17th 2009, 05:47 AMmathaddict
- Feb 17th 2009, 05:59 AMGrandadBinomial Coefficients
Hello teddybear67Yes, it does look rather a mess, doesn't it?

The working goes like this:

(I assume you agree that this is correct!)

Now the on the top and bottom cancel immediately. Then notice that the term on the top = . So it cancels with the term on the bottom to leave on the top.

Similarly the term on the bottom is . So it cancels with the term on the top to leave on the bottom.

Hence

... etc

I have checked my answer using an Excel spreadsheet (see the attached) and it is correct! So the answer in the book is wrong (nothing new there!).

Grandad - Feb 17th 2009, 06:05 AMteddybear67
lol i assumed that your

is correct, but i double checked and its supposed to be 3/2 . sorry!!

but yea, i understand your workings and managed to get the hang of it. thanks alot grandad!!! ^^ - Feb 17th 2009, 06:16 AMGrandadBinomial Coefficients
Hello teddybear67Ah, I see where comes from now. Of course, it depends which way round you're expanding the binomial. Your original question has the expression as . And for this the answer is , and the equal coefficients are the 7th and 8th.

But if you expand it the other way round , then the equal coefficients are the (19 - 7)th and (19 - 8)th i.e. the 12 th and 11th.

It's all so simple really.

Grandad

- Feb 17th 2009, 06:23 AMteddybear67
yepyeps, thanks much much again grandad !(Rofl)