1. Use the c-N definition of the limit of a sequence to show the following: 2n - 1 2n - 1 (i) lim COIN (ii) lim = 0 n-+00 3n + 2 n-+0 3n2 + 2 2. Let a be a real number. Prove that if an = a for all n E N, then lim an = a 7-+00 3. Prove that if lim an = L, for some real number L, then 7-+00 lim |an ) = |L| 1-+00 ( Hint: Use the reverse triangle inequality) 4. Let L and K be real numbers. Prove the following two statements (i) If an 0, the inequality Jan - L|