In: Advanced Math
1.Prove the following statements:
.
(a) If bn is recursively defined by bn =bn−1+3 for all integers n≥1 and b0 =2,
then bn =3n+2 for all n≥0.
.(b) If cn is recursively defined by cn =3cn−1+1 for all integers n≥1 and c0 =0,
then cn =(3n −1)/2 for all n≥0.
.(c) If dn is recursively defined by d0 = 1, d1 = 4 and dn = 4dn−1 −4dn−2 for all integers n ≥ 2,
then dn =(n+1)2n for all n≥0.