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- Homework Statement
- No homework.. I dont know why was moved...

- Relevant Equations
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**Summary::**How to know which one is bigger when n goes to infinity?

$$ \sum_{n=1}^\infty \frac {1} {\sqrt {n}(\sqrt {n+1}+\sqrt {n-1})} $$

And:

$$ \sum_{n=1}^\infty \frac {1} {\sqrt {n}(\sqrt {n}+\sqrt {n})} $$

I thought at first that the second one is bigger, although, I came to realize, to my mistake, that the first one is actually bigger.

How do I know which is the bigger one at numbers like those?

EDIT:

You can think of it like that:

$$\sqrt {n-1}+\sqrt{n+1} < \sqrt{2n}$$

Why is it like that? That is my problem to understand

**[Mentor Note -- Thread has been moved from the technical forums to the schoolwork forums]**

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