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Explain the conditions under which Radious of Convergence of Power Series is infinite. Explain what will happen?
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- Give an example of a series that converges by the integral test.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, divergesSolve for the valve of IL that malkes the series converge? nk
- 3. Find the interval of convergence for the power series 3" Vn Make sure to check the end points of the interval. Please state which tests you use.Determine whether the series is absolutely convergent, conditional convergent or divergent. Make sure to show detail step by step solutions. Make sure to name the test that you are using to do this problem, example: integral test, comparison test, alternating series test, root test, etc. n=1 (−1)n-³ √nI know to find the sum in an infinite geometric series using S=1/1-r, that it converges if -1<r<1, but what can we say if r=1? Would the sum not exist (diverges)? Would another method have to be used?
- give an example of a power series with an interval of convergence of -5<x<3 or state why no such power existsdoes this series converge?A pendulum is released and swings until it stops. If it passes through an arc of 8 inches in the first pass, and if on each successive pass it travels 3434 the distance of the previous pass, how far will it travel before stopping?