(a) Prove by the Principle of Mathematical Induction that 9n 2 is divisible by 7...

 

Transcribed Image Text:

(a) Prove by the Principle of Mathematical Induction that 9n – 2" is divisible by 7 for any n EN+ (7 Marks) (b) Prove by contradiction: For any m e N+, if m? is divisible by 3 then m is divisible by 3 (7 Marks) (c) Consider the sequence of real numbers r, = 2 + Prove by definition that rn converges to 2 as n → 0 (a) Prove by the Principle of Mathematical Induction that 9n – 2" is divisible by 7 for any n EN+ (7 Marks) (b) Prove by contradiction: For any m e N+, if m? is divisible by 3 then m is divisible by 3 (7 Marks) (c) Consider the sequence of real numbers r, = 2 + Prove by definition that rn converges to 2 as n → 0