The series n5 +2 √n13 +8 Convergent O Divergent O Cannot Be Determined A test that will NOT determine whether this series is convergent or divergent is (choose all that apply): Onth term test comparison test Olimit comparison test ratio test integral test

Which method would you use to determine whether the series √nª +1 n³+n Σn=1 converges or diverges? We will use Alternating series procedure, since the terms in this series have (-1)" expression multiplying the ratio We will use limit comparison test and compare this series with the series and therefore the series is convergent! 0 00 00 00 00 We will use Integral test, since integral of the terms seems fairly easy We will use limit comparison test and compare this series with the series 100 1 and therefore the series is convergent! n² We will use Ratio test, since the terms have ratios and expressions that can easily cancel. We will use Root test, since the n-th root of this expression will simplify the general term, and therefore this series is Absolutely Convergent This series diverges, since the terms don't have limit = 0 We will use limit comparison test and compare this series with the series, and therefore the series is divergent! This series converges, since the terms have limit…

Consider the series > Evaluate the the following limit. If it is infinite, type "infinity" or "inf". If it does not exist, type "DNE". (5n)! n=1 аn+1 lim = L An Answer: L What can you say about the series using the Ratio Test? Answer "Convergent", "Divergent", or "Inconclusive". Answer: choose one Determine whether the series is absolutely convergent, conditionally convergent, or divergent. Answer "Absolutely Convergent", "Conditionally Convergent", or "Divergent". Answer: choose one

Power series can be used to evaluate certain infinite series. An example is ∞Σ n=1 n/5^(n-1)   a) Find a power series representation of 1/(1-x)^2 by differntiating the power series representation of 1/(1-x). What is the interval of convergence for the power series of 1/(1-x)^2?   b) Use the your awnser in part (a) to find the sum of ∞Σ n=1 n/5^(n-1).  Also, to clear up any confusion, infinity is supposed to be on top and n=1 is on the bottom.