Solution Found!
Product of power series Let a. Multiply the power series
Chapter 8, Problem 65AE(choose chapter or problem)
Product of power series Let
\(f(x)=\sum_{k=0}^{\infty} c_{k} x^{k}\) and \(g(x)=\sum_{k=0}^{\infty} d_{k} x^{k}\0.
a. Multiply the power series together as if they were polynomials, collecting all terms that are multiples of 1, x, and \(x^{2}\). Write the first three terms of the product f(x)g(x).
b. Find a general expression for the coefficient of \(x^{n}\) in the product series, for n = 0, 1, 2,....
Questions & Answers
QUESTION:
Product of power series Let
\(f(x)=\sum_{k=0}^{\infty} c_{k} x^{k}\) and \(g(x)=\sum_{k=0}^{\infty} d_{k} x^{k}\0.
a. Multiply the power series together as if they were polynomials, collecting all terms that are multiples of 1, x, and \(x^{2}\). Write the first three terms of the product f(x)g(x).
b. Find a general expression for the coefficient of \(x^{n}\) in the product series, for n = 0, 1, 2,....
ANSWER:Solution 65AEStep 1:Given thatLet Step2:To finda. Multiply the power series together as if they were polynomials collecting all terms that are multiples of 1. x. and x2 . Write the first three terms of the product f(x)g(x).b. Find a general expression for the coefficient of an