Calculate Limit of Sequence: n -> ∞

[aid]

Homework Statement

Calculate the limit of a given sequence for $$n \rightarrow \infty$$:

$$\frac{1 - 2 + 3 - ... + (2n - 1) - 2n}{\sqrt{n^2 + 1}}$$

The Attempt at a Solution

The correct answer seems to be -1. I've tried to apply the Stolz theorem but failed to compute $$\sqrt{(n + 1)^2 + 1} - \sqrt{n^2 + 1}$$. Will be grateful for any hints.

 

[Tedjn]

Simplify the numerator and see if you can incorporate it somehow into the a square root. You should not need to use Stolz's theorem.

 

[Karlx]

I agree with Tedjn.
No need of Stolz's theorem.
Just try to write the numerator in a compact expression.