Part (a): Show that, for any a, b, n = bn-kak = b + br-a + b-a + b-a+. + ban-1 + an k=0 [Hint: multiply both sides by b-a.] Part (b): Show that, for any a, n ak = 1 +a+a + a + ... + a- + a = k=0 Part (c): Use the above result to show that, for |a| < 1, Part (d): Show that 00 k=0 = k=1 1 - a d=1 ak a 1-a br+1 b an+1 a 1-a+1 1-a = an+1 6+1 a- -b