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## Homework Statement

Consider the sequence given by [itex]b_{n} = n - \sqrt{n^{2} + 2n}[/itex]. Taking [itex](1/n) \rightarrow 0[/itex] as given, and using both the Algebraic Limit Theorem and the result in Exercise 2.3.1 (That if [itex](x_n) \rightarrow 0[/itex] show that [itex](\sqrt{x_n}) \rightarrow 0[/itex]), show [itex]\lim b_{n}[/itex] exists and find the value of the limit.

## Homework Equations

[itex]b_{n} = n - \sqrt{n^{2} + 2n}[/itex] and [itex](1/n) \rightarrow 0[/itex]

## The Attempt at a Solution

Does the [itex](1/n) \rightarrow 0[/itex] imply that I should put b

_{n}in the form 1/n? Going in that direction, I'm stuck at [tex]\frac{-2n}{n + \sqrt{n^{2} + 2n}}[/tex] Am I going in the right direction? And if so, any hints on how to further manipulate what I have? I'm self-studying, and do not have a professor or mentor or anything to give me a bit of direction.