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.
A power series is a mathematical expression that represents a function as an infinite sum of terms. When the variable in the series is very large, it means that the value of that variable is approaching infinity.
The convergence of a power series when the variable is very large can be determined by using the Ratio Test or the Root Test. These tests compare the infinite series to a geometric series with a known convergence value.
Yes, a power series can diverge when the variable is very large. This occurs when the terms of the series do not approach zero as the variable approaches infinity, making it impossible for the infinite sum to have a finite value.
Power series can be used to approximate functions when the variable is very large by truncating the series to a finite number of terms. This finite sum can then be used as an approximation for the function, with the accuracy increasing as more terms are included.
Yes, power series with large variables have many real-world applications, such as in physics, engineering, and economics. They can be used to model and approximate complex phenomena, such as the behavior of gases at high temperatures or the growth of populations over time.