Question: These questions are from my tutorial session but didn't understand well! need some help 4. Consider the sequence dened recursively by s0 = 0, s1

These questions are from my tutorial session but didn't understand well! need some help

4. Consider the sequence dened recursively by s0 = 0, s1 = 1, s2 = 0; sn := sn3 + sn2 sn1 for n 3 .

(a) Calculate s3, s4 and s5 and make a guess as to the general form of sn.

(b) Use induction to prove that your guess is correct.

8. For a positive integer n, let p(n) be the statement "n2 3n is odd".

(a) Show that p(n) p(n + 1) for each positive integer n.

(b) For which numbers n is p(n) true?

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