The discussion focuses on finding the first three non-zero terms in the series expansion of the logarithmic function ln(5+p) for small values of p. The correct approach involves rewriting the function as ln(5[1+(p/5)]) and applying the properties of logarithms. This leads to the series expansion of ln(1+(p/5)), which can be expressed as (p/5) - (1/2)(p/5)^2 + (1/3)(p/5)^3. The accuracy of the expansion is contingent upon the proximity of p to -4, but the task specifically requires only the first three non-zero terms.
PREREQUISITESStudents in calculus, mathematicians focusing on series expansions, and anyone interested in the applications of logarithmic functions in mathematical analysis.
Well, the accuracy, for any finite polynomial expansion, deteriorates as p gets farther from -4 but is the accuracy really relevant? You are only asked to "Find first three non zero terms".seboastien said:Homework Statement
Find first three non zero terms in series expansion where the argument of funstion is small
ln(5+p)
Homework Equations
The Attempt at a Solution
The only way I could think how to do this is by saying ln(5+p) = ln(1+(4+p)) and expanding to
(4+p)- 1/2(4+p)^2 + 1/3(4+p)^3 - ... however, I imagine that this would only work if p was approx -4.