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Need Help with Binomial expansion coefficient q

I have to find the coefficient of x^17 for
(6x513x3)21 \displaystyle \left ( 6x^5-\frac{1}{3x^3} \right )^{21}

So first I write it out

(6x513x3)21=21!k!(21k)!(6x5)21k(13x3)k \displaystyle \left ( 6x^5-\frac{1}{3x^3} \right )^{21} = \frac{21!}{k!(21-k)!}(6x^5)^{21-k} \left (\frac{-1}{3x^3} \right )^k

After re arranging I get 105-8k=17 so K isnt a very nice number!

Ive used this method on other expansions and its been fine?

Any help would be appreciated, thank you :smile:
Reply 1
Original post by tigerz
I have to find the coefficient of x^17 for
(6x513x3)21 \displaystyle \left ( 6x^5-\frac{1}{3x^3} \right )^{21}

So first I write it out

(6x513x3)21=21!k!(21k)!(6x5)21k(13x3)k \displaystyle \left ( 6x^5-\frac{1}{3x^3} \right )^{21} = \frac{21!}{k!(21-k)!}(6x^5)^{21-k} \left (\frac{-1}{3x^3} \right )^k

After re arranging I get 105-8k=17 so K isnt a very nice number!

Ive used this method on other expansions and its been fine?

Any help would be appreciated, thank you :smile:


your method is correct

you get k=11
Reply 2
Original post by TeeEm
your method is correct

you get k=11


*facepalm* I did the difficult bit and messed up with the re arrangement >.<

Thank youu
(edited 9 years ago)
Reply 3
Original post by tigerz
*facepalm* I did the difficult bit and messed up with the re arrangement >.<

Thank youu


no worries

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