Subject: Power series representations Is there a systematic way of finding a power series representation of a function? I understand that you have to manipulate the function so that it is of the form 1/(1x), but beyond that I am lost.
Grace There is a systematic way of finding a power series representation of some functions that is usually learned in a second university calculus class. If, however, you can manipulate the function so that it is in the form 1/(1x) the procedure is more straightforward. If you divide 1x into 1 using long division you see a power series representation which is the geometric series wirh first term 1 and the common ratio x. This is not the end of the story as the series converges only if x < 1. An explanation of why this is true can be found in Infinite Geometric Series, the answer to a previous question on series. I hope this helps,Harley
