A set S consists of strings obtained by juxtaposing one or more copies of 1110 and 0111. Use mathematical induction to prove that for every integer  n ≥ 1,  if s is any string in S that has length 4n, then the number of 1's in s is a multiple of 3.

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Q: y. Use strong induction to prove that if n EN and n> 10

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A: Given: fn=fn+1+fn+2  for n=1,2,3, ...with f1=f2=1To prove: fn <2n ∀ n∈ℤ+Let for n=1, 21<2 and…

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A: b).we have,an=1+-1nan-2=1+-1n-2an-2=1+-1n-12an-2=1+-1nThus,an=an-2=an-4=an-6=...=so onagain,…

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A: Given The recurrence relation is an+1=an10+3 ;  a0=10

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A: we have to solve by using mathematical induction

Q: Let fn be the n-th Fibonacci number of Example 3c in 8.1, k=n k=n Σ'=1+2+...+ B₁=k²= 1² +2²+. k=1…

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Q: A sequence {an} is defined recursively by a1 = 6, a2 = 8, and an = 2an−1 − an−2 for n ≥ 3. Prove…

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Q: Recall the definition of Fibonacci numbers: • F1 = 0 • F2 = 1 • Fn = Fn−1 + Fn−2 For example, the…

A: Given Fn=φn-1-(1-φ)n-15, where φ=1+52 So Fn=φn-1-(1-φ)n-15=151+52n-1-1-52n-1…

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Q: 1) Use mathematical induction to show that any postage of at least 28 cents can be obtained using 5c…

A: Image is attached with detailed explanation.

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A: For n = 1,       LHS = 4 [only 1 term]      RHS = 2.12 + 2.1 = 2.1 + 2.1 = 4 Hence, LHS = RHS.  So,…

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Q: Consider the se quence defined recursively as follows do =2 ak =yak-itl © find di,a2,93,a4 ,as ®…

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Q: 1. а) Suppose that fis defined recursively by: f(0) = 5 and f(n+1) = 2 fin + 5. Find (1). A2). A3)…

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