I need help simplifying this power series.

(x^2-1)sum_{n=2}^{infty}[n(n-1)C_nx^{n-2}]+4x\sum_{n=1}^{infty}[nC_nx^{n-1}]+2\sum_{n=0}^{infty}[C_nx^{n}]

I need to get everything under 1 summation and so that $$x^{n}$$ pulls out but I cannot figure out how to do it.

Thanks

Question

I need help simplifying this power series.

(x^2-1)sum_{n=2}^{infty}[n(n-1)C_nx^{n-2}]+4x\sum_{n=1}^{infty}[nC_nx^{n-1}]+2\sum_{n=0}^{infty}[C_nx^{n}]

I need to get everything under 1 summation and so that $$x^{n}$$ pulls out but I cannot figure out how to do it.

Thanks

anonymous · Answer

$$(x^2-1)\sum_{n=2}^{infty}[n(n-1)C_nx^{n-2}]+4x\sum_{n=1}^{infty}[nC_nx^{n-1}]+2\sum_{n=0}^{infty}[C_nx^{n}]$$

anonymous · Answer

This is for Diff Equ

anonymous · Answer

Yeah, im not looking for x really. You use the fact that $$\sum_{i}^{\infty}[K_nx^n]=0 $$ means that K_n = 0 and find y (which is where we get these power series) in terms of a new power series.

loser66 · Answer

@satellite73