Explain step by step and thoroughly. a) Prove that: nN,i=0ni2i=(n1)2n+1+2. b) Consider the sequence (si)iZ+defined by s1=1 and: n2..+ ,sn=2sn1+n. Show that sn=4sn2+(2n+n)2 and sn=8sn3+(4n+2n+n)(42+2). Likewise, express sn in terms of sn4 and n, and then in terms of sn5 and n. c) Using a) and b), can you guess sn in terms of sni,n and i? What expression do you get for sn when i=n1 ? Verify it by induction..