(a) Prove by the Principle of Mathematical Induction that n > (2i 1) = n?...

 

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(a) Prove by the Principle of Mathematical Induction that n > (2i – 1) = n? i=1 (7 Marks) (b) Prove by contradiction that there are infinitely many prime numbers. (7 Marks) (c) Knowing that sequence of real numbers rn = converges n to 0 as n → ∞, use the Sandwich Theorem to determine 1 lim (2 + (a) Prove by the Principle of Mathematical Induction that n > (2i – 1) = n? i=1 (7 Marks) (b) Prove by contradiction that there are infinitely many prime numbers. (7 Marks) (c) Knowing that sequence of real numbers rn = converges n to 0 as n → ∞, use the Sandwich Theorem to determine 1 lim (2 +