Math Help - Sequence limit problem

1. Sequence limit problem

I have to show that if

$a_0+a_1+a_2+...+a_p=0$ then $\lim_{n\rightarrow\infty} (a_0\sqrt{n}+a_1\sqrt{n+1}+a_2\sqrt{n+2}+...+a_p \sqrt{n+p})=0$

Any ideas?

2. Re: Sequence limit problem

$a_p=-\sum_{k=0}^{p-1}a_k$ so $\sum_{k=0}^pa_k\sqrt{n+k}=\sum_{k=0}^{p-1}a_k\frac{k-p}{\sqrt{n+k}+\sqrt{n+p}}$.