- (i) Prove by induction that, for \(n \in \mathbb { Z } ^ { + }\)
$$\sum _ { r = 1 } ^ { n } \frac { 2 r ^ { 2 } - 1 } { r ^ { 2 } ( r + 1 ) ^ { 2 } } = \frac { n ^ { 2 } } { ( n + 1 ) ^ { 2 } }$$
(ii) Prove by induction that, for \(n \in \mathbb { Z } ^ { + }\)
$$f ( n ) = 12 ^ { n } + 2 \times 5 ^ { n - 1 }$$
is divisible by 7
| VILU SIHI NI JIIIM ION OC | VIUV SIHI NI III M M I ON OO | VIAV SIHI NI JIIIM I ION OC |
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| VIXV SIHIANI III IM IONOO | VIAV SIHI NI JYHAM ION OO | VI4V SIHI NI JLIYM ION OO |
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