last generating function question.

stumped765 · #1 $Old$ November 5th, 2009, 05:31 PM

Im confused by generating functions. Theres the 5 main "rules" that u need to manipulate the expressions given to determine the sequence.

(4x-1)^3 at first glance i think to use the binomial but the form of it is (1+x)^n = nC0 + nC1 x + nC2 x^2 + ...

but my issue is i assume that i cant just ignore that they arent of the same form.. but then im lost.
If anyone can explain it to me id be grateful I really want to actually understand.

Drexel28 · #2 $Old$ November 5th, 2009, 06:51 PM

Quote:

Originally Posted by stumped765 $View Post$

Im confused by generating functions. Theres the 5 main "rules" that u need to manipulate the expressions given to determine the sequence.

(4x-1)^3 at first glance i think to use the binomial but the form of it is (1+x)^n = nC0 + nC1 x + nC2 x^2 + ...

but my issue is i assume that i cant just ignore that they arent of the same form.. but then im lost.
If anyone can explain it to me id be grateful I really want to actually understand.

$\left(4x-1\right)^3=-\left(1-4x\right)^3=-\left(1+\left(-4x\right)\right)^3$ . If you let $z=-4x$ this becomes what you desire.