Solution Found!
Powers of x multiplied by a power series Prove that if
Chapter 8, Problem 63AE(choose chapter or problem)
QUESTION:
Powers of x multiplied by a power series Prove that if \(f(x)=\sum_{k=0}^{\infty} c_{k} x^{k}\) converges on the interval I, then the power series for \(x^{m} f(x)\) also converges on I for positive integers m.
Questions & Answers
QUESTION:
Powers of x multiplied by a power series Prove that if \(f(x)=\sum_{k=0}^{\infty} c_{k} x^{k}\) converges on the interval I, then the power series for \(x^{m} f(x)\) also converges on I for positive integers m.
ANSWER:Solution 63AE
Step 1:
Given that
converges on the interval I