single power series...

**slapmaxwell1** · April 9th 2011, 01:15 AM

i was wondering if someone could check my work...

i am supposed to rewrite the following series as a single power series...

$4\sum_{n=2}^{\infty }n(n-1)c_{n}x^{n-2}-3\sum_{n=1}^{\infty}nc_{n}x^{n-1}+\sum_{n=0}^{\infty}c_{n}x^{n}$

here is what i got as an answer...did i do it right?

$8c_{2}-3c_{1}+c_{0}+4\sum_{k=1}^{\infty}(k+2)(k+1)c_{k+2} x^{k}-3\sum_{k=1}^{\infty}(k+1)c_{k+1}x^{k}+\sum_{k=1}^{ \infty}c_{k}x^{k}$

**Danny** · April 10th 2011, 07:50 AM

Looks good to me but you could have done

$4\sum_{k=0}^{\infty}(k+2)(k+1)c_{k+2}x^{k}-3\sum_{k=0}^{\infty}(k+1)c_{k+1}x^{k}+\sum_{k=0}^{ \infty}c_{k}x^{k}$ .

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