- #1

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## Homework Statement

Hey, I'm trying to determine the following limit:

[tex]\lim_{n \rightarrow \infty}\sum_{j=0}^k{a_j\sqrt{n+j}}[/tex]

where

[tex]\sum_{j=0}^k{a_j}=0[/tex]

## The Attempt at a Solution

I tried to go this way:

[tex]\lim_{n \rightarrow \infty}\sqrt{n+k}\sum_{j=0}^k{a_j\frac{\sqrt{n+j}}{\sqrt{n+k}}}[/tex]

but still I get 0*infinity, which is undefined.