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**1. Homework Statement**

Estimate [tex]\sum^{\infty}_{n=1}n^{-3/2}[/tex] to within 0.01

**2. Homework Equations**

[tex] \int^{\infty}_{n+1}f(x)dx\leq R_{n} \leq \int^{\infty}_{n}f(x)dx[/tex]

**3. The Attempt at a Solution**

So my strategy was using the above formula to find Rn, where Rn = 0.01 or 1/10^2. Then that will give me the n value, which I can use to find the partial sum. It worked for all other problems but when I looked at the solution manual, they are doing something weird and I can't understand.

[tex]

\int^{\infty}_{x}x^{-3/2}dx= \left[ -2x^{-1/2}\right]^{\infty}_{x}[/tex]

and if I do the appropriate substitution etc.. I get [tex]\frac{2}{\sqrt{x}} = \frac{1}{10^2}[/tex], which give me a x or n value of 40000. A bit too big considering the textbook has a answer of like 14. What I am doing wrong? Thanks.

Here is the textbook's solution, which I don't get at all..

http://p3t3rl1.googlepages.com/texsolution.jpg

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