- (i) Prove by induction that, for \(n \in \mathbb { Z } ^ { + }\)
$$\sum _ { r = 1 } ^ { n } \left( 4 r ^ { 3 } - 3 r ^ { 2 } + r \right) = n ^ { 3 } ( n + 1 )$$
(ii) Prove by induction that, for \(n \in \mathbb { Z } ^ { + }\)
$$f ( n ) = 5 ^ { 2 n } + 3 n - 1$$
is divisible by 9