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## Main Question or Discussion Point

**1. Homework Statement**

Does anyone have this book? I have some questions about chapter 3.

**2. Homework Equations**

**3. The Attempt at a Solution**

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Does anyone have this book? I have some questions about chapter 3.

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quasar987

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This is an example of what is called a "telescoping series".

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Yes I figured that out before you posted and deleted that part of the post because it was embarrassing.

This is an example of what is called a "telescoping series".

What about [itex]\sum_n \frac{\sqrt{n+1}-\sqrt{n}}{n} [/itex]. This definitely does not telescope. But both 1/n and \sqrt{n+1}-\sqrt{n} diverge so it is pretty clear that their product will. But what test should I use? The ratio test is too hard too evaluate. The root test is even harder to evaluate. What series can I compare it to?

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NateTG

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Hmm, is any term in that series larger than:What about [itex]\sum_n \frac{\sqrt{n+1}-\sqrt{n}}{n} [/itex]

[tex]\frac{1}{2n^{\frac{3}{2}}}[/tex]

(This falls out easily with a little algebra.)

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No (but I am not sure why you have the 2 there).Hmm, is any term in that series larger than:

[tex]\frac{1}{2n^{\frac{3}{2}}}[/tex]

So, does anyone have the book?

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