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## Homework Statement

Find a, sucht that:

[tex]

\lim_{ x \to \infty }( a \sqrt{n+2} - \sqrt{n+1} ) ) = \infty(a+1)

[/tex]

Now, I want this sequence to have the limit 0. The first impule is to say that a+1 = 0 and hence a = -1. But if I do this I get [tex] \infty 0 [/tex] which can't be determined. The paradox is that a = -1 works, because if a = -1 then indeed the sequence tends to 0. So, what am I missing? Can you help me, please?

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