on - cos(n) Consider the two methods for checking whether the sequence { a, } _, given by a, = converges, 2n and decide whether they are carried out correctly. Method 1: 6n2 - 1 On - cos(n) On + 1 We apply the Squeezing Theorem: for each n, and 2n 2n 2n Gin - 1 On + 1 On - cos (n) lim lim 3. Therefore lim = 3 as well, so the sequence converges. 2ra 2n 2n Method 2: on - cos(n) 6 + sin(n) We apply I'Hopital's Rule: lim lim = 3. Therefore the sequence converges. 2n 2