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