Section 10.7 Power Series

Make sure you read the questions very carefully and see on what its being asked for. Please be very serious careful with this assignment.

Feedback: #1: A similar issue is here. How is the limit of (4n+1)/(12n + 5) computed? This part should have some justification here. #3: It's unclear what's going on here, but the limit comparison test is not being applied correctly in this situation. I feel like the first attempt was closer to what's going on and why does the compared series diverge? This must be included when using limit comparison test.

MATH 1522: SECTION 10.7 WRITTEN ASSIGNMENT In this assignment, we go over the process for finding the interval of convergence for a power series. Consider the power series defined by f(x) = (x - 2)" (4n + 1)3n n=0 1. Apply the ratio or root test to find the radius of convergence. Use algebra to find the interval of convergence (excluding the endpoints for now). Show all the steps of the compu- tations. 2. Plug in the left endpoint (smaller of the two numbers in the interval) into the power series to obtain a series. Determine whether the resulting series converges or diverges. State the convergence test being used and show all the steps for the needed computations. 3. Plug in the right endpoint (larger of the two numbers in the interval) into the power series to obtain a series. Determine whether the resulting series converges or diverges. State the convergence test being used and show all the steps for the needed computations. Finally, state the interval of convergence (including possible endpoints)