
single power series...
i was wondering if someone could check my work...
i am supposed to rewrite the following series as a single power series...
$\displaystyle 4\sum_{n=2}^{\infty }n(n1)c_{n}x^{n2}3\sum_{n=1}^{\infty}nc_{n}x^{n1}+\sum_{n=0}^{\infty}c_{n}x^{n}$
here is what i got as an answer...did i do it right?
$\displaystyle 8c_{2}3c_{1}+c_{0}+4\sum_{k=1}^{\infty}(k+2)(k+1)c_{k+2} x^{k}3\sum_{k=1}^{\infty}(k+1)c_{k+1}x^{k}+\sum_{k=1}^{ \infty}c_{k}x^{k}$

Looks good to me but you could have done
$\displaystyle 4\sum_{k=0}^{\infty}(k+2)(k+1)c_{k+2}x^{k}3\sum_{k=0}^{\infty}(k+1)c_{k+1}x^{k}+\sum_{k=0}^{ \infty}c_{k}x^{k}$.