Binomial Questions (1 Viewer)

[Kutay]

I have a question on the follow things... i was wondering if this is right in trying to solve these types of questions...

for example say when you are trying to find the independent term of x, u do that thingy to first find r ... then put it back into the formula.

but when you get a question asking find the coefficent of x^10 can you do it that way.... because i remeber doing a question asking to find the coefficent of x^3 and it worked but when doing this x^10 one it didn't anyhow this is the question.......

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Find the coefficient of x^10 in the expansion of (1 + 2x)^18

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also just wondering about the type of question how to do this...

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Find the greatest coefficent of the expansion of (3 + 2x)^ 20

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Thankyou

 

[FinalFantasy]

"Find the coefficient of x^10 in the expansion of (1 + 2x)^18 "
First just write the general term;
18Ck(1)^(18-k)(2x)^k=18Ck (2)^k x^k
for the power of x to be 10, u set k=10
so the coefficient of x^10 would be 18C10 * (2)^10=calculator


"Find the greatest coefficent of the expansion of (3 + 2x)^ 20"
general term: 20Ck (3)^(20-k)(2x)^k=20Ck 3^(20-k) 2^k x^k
now general coefficient t_k=20Ck 3^(20-k) 2^k
and
t_(k+1)=20C(k+1) 3^(20-(k+1) ) 2^(k+1)
=20C(k+1) 3^(19-k) 2^(k+1)

t_(k+1) \ t_k=20Ck 3^(20-k) 2^k \ 20C(k+1) 3^(19-k) 2^(k+1)
after u simplify that, then write t_(k+1)\t_k > 1
then work out the inequality for k
den u got ur greatest coefficient

 

[Kutay]

thankyou....