Find the sequence a k </msub> for generating function (

Timiavawsw9

Timiavawsw9

Answered question

2022-05-21

Find the sequence a k for generating function ( 1 x 3 1 x ) n .
We know that 1 ( 1 x ) n = k = 0 ( k + n 1 n 1 ) x k
I also worked out ( 1 x 3 ) n using the binomial theorem and got ( 1 x 3 ) n = i = 0 ( 1 ) i ( n n i ) x 3 i .
I'm not sure what to do with these to get a k from k = 0 a k x k or if these are even what I need to solve the problem

Answer & Explanation

Sasha Pacheco

Sasha Pacheco

Beginner2022-05-22Added 10 answers

Explanation:
( 1 x 3 1 x ) n = ( ( 1 x ) ( 1 + x + x 2 ) 1 x ) n = ( 1 + x + x 2 ) n

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