Answered

Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

Find the function to which the given series converges within its interval of convergence. Use exact values. 1 3 x 9 x 2 2 ! 27 x 3 3 ! 81 x 4 4 ! 243 x 5 5 !

Sagot :

LammettHash

It looks like the series could be

[tex]\displaystyle 1 + 3x + \frac{9x^2}{2!} + \frac{27x^3}{3!} + \cdots = \sum_{n=0}^\infty \frac{3^nx^n}{n!} = \sum_{n=0}^\infty \frac{(3x)^n}{n!}[/tex]

Recall that

[tex]\displaystyle e^x = \sum_{n=0}^\infty \frac{x^n}{n!}[/tex]

It follows that the given series is the power series expansion for [tex]\boxed{e^{3x}}[/tex].

We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.