# Mathematical problem from the course of reactor physics

1. Jan 24, 2009

### phys_g

Hello everybody,

This problem is from "Elementary Introduction to Nuclear Reactor Physics" by Liverhant,
I will be thankful for any help,because I'm really stuck on it :(
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(6-11)Calculate the smallest value of A for which the maximum fractional energy loss can be approximated by 4/A to within an error of 1%.
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the ans. should be 200.

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the relevant equation is:

$$\ ( \frac{\Delta E }{E0} )max.=\frac{4}{A} -\frac{8}{A^{2}}+\frac{12}{A^{3}}-\frac{16}{A^{4}}+... = (\frac{4}{A})(1-\frac{2}{A}+\frac{3}{A^{2}}-...)$$

it looks easy but I couldn't get the right answer...
I tried to differentiate this eq. then equate the outcome with zero (to get the smallest value of A), but also I might need to study the series convergence (the radius of convergence must take the value of 1% ...right?)..I'm confused and don't know how to start..because non of these ideas got me the right answer.

I'll appreciate it if anyone can help me in solving this problem either analytically or numerically.

Last edited: Jan 24, 2009
2. Jan 24, 2009

### Dick

The series is alternating in sign and the terms are decreasing in magnitude. An error bound for such alternating series is that if S is the sum of the whole series with terms a_i, and S_k is the sum of the first k terms, then |S-S_k|<=|a_{k+1}|.

3. Jan 25, 2009

Thanks Dick!