a) Prove that: Vne N, 2i2 = (n 1)2+1 +2. b) Consider the sequence (Si)ie Z+ defined by Si=1 and: Vne 2..too, Sn=2Sn_1+n. Show that sn=4sn_2+(2n+n)-2 and sn=8Sn_3+(4n+2n+n)-(4x2+2). Likewise, express Sn in terms of Sn_4 and n, and then in terms of Sn_s and n. c) Using a) and b), can you guess Sn in terms of Sn_i, n and i? What expression do you get for Sn when i=n12 Verify it by induction