Proofs involving Convergent and Divergent sequences Prove the following: (a) lim 0 ([b) lim n1/3 =0 (c) lim 2n-1 3n+2 (d) lim n+6 712-6 .= 0 Determine the limits of the following sequences, and then prove your claims. (a) an = n2+1 n (b) bn = 7n-19 3n+7 (c) on = An+3 (d) dn = 2n+4 5n+2 (e) Sn = _ sinn Let (Sn) be a sequence of nonnegative real numbers, and suppose lim sn = 0. Prove lim on = 0. This will complete the proof for Example 5. Let (tn) be a bounded sequence, i.e., there exists M such that (tn | - M for all n, and let (Sn) be a sequence such that lim s, = 0. Prove lim(Sntn) = 0