Power series when variable is very large

AI Thread Summary
To find the first three non-zero terms in the series expansion for ln(1+e^-z) when z is very large, the expression can be simplified to ln(1+e^(-1/z)e^((1/z)(z^2 - 1))). A suggested approach involves referencing series expansions from reliable mathematical resources, such as the one on MathWorld. It is important to verify that the conditions for convergence are met for the series being used. The discussion emphasizes the need for careful manipulation of the exponential terms to derive the desired series expansion. Ultimately, the goal is to accurately compute the series expansion for large values of z.
seboastien
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Homework Statement



Find first three non zero terms in series expansion for ln(1+e^-z) when z is very large


Homework Equations






The Attempt at a Solution



I've got as far as ln(1+e^(-1/z)*e^((1/z)(z^(2) - 1))

not sure where to go from here
 
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seboastien said:
Find first three non zero terms in series expansion for ln(1+e^-z) when z is very large

Maybe series (19) on this page http://mathworld.wolfram.com/SeriesExpansion.html" would be a good start. Just check that your conditions satisfy the inequality so the series will be sure to converge.
 
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