QUESTION THREE(20 MARKS) a) Use mathematical induction to prove that 57 divide n=0 7n+2+8n+1 (6 marks)...

 

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QUESTION THREE(20 MARKS) a) Use mathematical induction to prove that 57 divide n=0 7n+2+8²n+1 (6 marks) b) Let a=195 and b=968. Use the division algorithm to find the gcd(a,b) and therefore find integers m and n such that d-am +bn c) Consider the third order homogeneous recurrence relation a, = 6a,-1 i. ii. Find the general solution Find the initial solution given a, = 3, a₁ = 4,a₂ = 12 (6 marks) +8a-3 -12a-2 (4 marks) (4 marks) QUESTION THREE(20 MARKS) a) Use mathematical induction to prove that 57 divide n=0 7n+2+8²n+1 (6 marks) b) Let a=195 and b=968. Use the division algorithm to find the gcd(a,b) and therefore find integers m and n such that d-am +bn c) Consider the third order homogeneous recurrence relation a, = 6a,-1 i. ii. Find the general solution Find the initial solution given a, = 3, a₁ = 4,a₂ = 12 (6 marks) +8a-3 -12a-2 (4 marks) (4 marks)

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The detailed answer for the above question is provided below a We can use mathematical induction to prove that 57 divides 7n2 82n1 for all negative in... View the full answer