MATH-M 212 Lecture Notes - Lecture 19: Partial Fraction Decomposition, Ratio Test, Polynomial Long Division
Document Summary
Use polynomial long division and fit to a geometric series centered at 0 that represents it. Section 9. 9 notes- representation of functions by power series. 3 ways to find a power series that represents a function: taylor/maclaurin formulas, polynomial long division, fit function to geometric series. What times 1 = 1? ; what times 1 = x? ; distribute each answer, subtract quantity, continue (technically infinite) Quotient: for geometric series, is true if. Do not have to check endpoints; geometrics follow , not. Find a power series centered at 2 to represent . Ex. o indicates center at 2 balances out in parentheses: series, interval of convergence: Use polynomial long division to find a power series centered at 2 to represent the same. Ex. function. o: does not match previous answer- long division only works when centered at 0. Operations with power series: applying may change interval of convergence, let and.
