2. Prove the limit ratio test (Corollary 3.8 in the notes): Suppose {an} is a sequence of nonzero real numbers and r(n) = |"n+1|. Suppose further that lim,+ r(n) = L. Show that (i) If L < 1, the series an converges absolutely. (ii) If L > 1, the series an diverges. Hint. This is a Corollary to the ratio test (Theorem 3.6 in the notes), so you should be using the ratio test in your proof. n→∞

Question 10 of 10 Find the general term of the sequence, starting with n = 1. Determine whether the sequence converges, and if so find its limit. If the sequence diverges, indicate that using the checkbox. (√2-VII), (√3-√12), (√4-√13),... An lim an 11-1+00 The sequence diverges. -/5 E ...