- #1

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## Homework Statement

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Use the Bounded Monotonic Sequence Theorem to prove that the sequence:

[tex] \{a_{i} \} = \Big\{ i - \sqrt{i^{2}+1} \Big\} [/tex]

Is convergent.

## Homework Equations

## The Attempt at a Solution

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I've shown that it has an upper bound and is monotonic increasing, however it is to my understanding that for me to use this theorem the sequence must be bounded (and of course have monotonicity) - i.e. have an upper and lower bound. I can't seem to show that this has a lower bound; even graphically, it just blows off to negative infinity. How should I proceed?