(x +1)"+1 Ln=0 _2"(n+1)

27) Determine whether the following series converges: € (k-1)* k=4

Can you solve this using the flow given for determination of integrating factor

12) There is one special “family” of series for which, if the series converges, we can determine the exact value of the series. This is the family where it really matters that we know the bounds of the summation. What family is this?

This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the slipped part Tutorial Exercise Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.) Step 1 (4x)" (an)! Recall the Ratio Test, which states that if a, is a series with nonzero terms, and lim 1, or lim 1 For any fixed value of x such that x 0, let a (4x)" (an)! and find lim 518 (4x)+1 lim 518 = lim (3(n+1)) 719 (a) (3n) (3n)! (4x)+1) = - (3(n+1))! 880.0 (-00,00) X Step 2 By the Ratio Test, the series converges if lim Submit Skip (you cannot come back) 518 1. Therefore, the series converges for x such that lim =, then, diverges

In the problem, find the circle and radius of convergence of the given power series: