5 6 12 Let s0, s1, s2, be defined by the formula (1) for all integers n 0 Show that this sequence satisfies the recurrence relation 1 1 5 6 29 Let F0, F1, F2, be the Fibonacci sequence Prove that (no need to use mathematical induction) 1, 1 2 2 1 2 Hint use the identity x2 y 2 (x y)(x y) ( 1)n n 5 6 12 Let s0, sl, s2, be defined by the formula S for all integers n0 Show that this sequence satisfies the recurrence relation IS, Sk 1 5 6 29 Let Fo, FI, F2, be the Fibonacci sequence Prove that (no need to use mathematical induction) For all integers k 21, F2 1 Fe 1 Fe 2 , Hint use the identity x2 (x y) (x y)

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Question: 5.6.12 Let s0, s1, s2, . . . be defined by the formula = (1) ! for all integers n 0. Show that this sequence

5.6.12 Let s0, s1, s2, . . . be defined by the formula = (1) ! for all integers n 0. Show that this sequence satisfies the recurrence relation: = 1 1 5.6.29 Let F0, F1, F2, be the Fibonacci sequence. Prove that: (no need to use mathematical induction) 1, +1 2 2 = 1 +2 Hint: use the identity x2 y 2 = (x-y)(x+y)

5.6.12 Let s0, s1, s2, . . . be defined by the

(-1)n n! 5.6.12 Let s0, sl, s2,... be defined by the formula S for all integers n0 Show that this sequence satisfies the recurrence relation:IS,-- Sk-1 5.6.29 Let Fo, FI, F2,... be the Fibonacci sequence. Prove that: (no need to use mathematical induction) For all integers k 21, F2.1- Fe-1 Fe#2 = , Hint: use the identity x2 = (x-y) (x+y)

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