- (i) Prove by induction that for \(n \in \mathbb { Z } ^ { + }\)
$$\sum _ { r = 1 } ^ { n } ( 3 r + 1 ) ( r + 2 ) = n ( n + 2 ) ( n + 3 )$$
(ii) Prove by induction that for all positive odd integers \(n\)
$$f ( n ) = 4 ^ { n } + 5 ^ { n } + 6 ^ { n }$$
is divisible by 15