8. Suppose that họ, h1, h2, . is a sequence defined as follows: ho = 1, h1 = 2, h2 = 3, %3D h = hx-1+hx-2+h=3 for each integer k > 3. a. Prove that h, < 3" for every integer n > ). b. Suppose that s is any real number such that s' > s +s+1. (This implies that 2 > s > 1.83.) Prove that h,

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A: Given,

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A: The solution is given below

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A: We prove this by strong Mathematical induction.

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A: As per our company guidelines we are supposed to answer only first three sub-parts. Kindly repost…

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A: I have given the proof in details

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A:

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A: Prove the following as follows.

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Q: 1. Consider the sequence {an}, where a, e [a, b] for all n e N. Show that is convergent.

A:

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A: topic - sequence and series

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A: I have proved using Apsilon delta definition

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A: Given Tn  =  2n2 - 5n +1 T1 = 2×12 - 5×1 + 1 = -2 T2 = 2×22 - 5×2 + 1 = -1 T3= 2×32 - 5×3 + 1 = 4…

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Q: Determine whether the sequence [In(k²-5)] 3k +4 00 k=1 converges or diverges.

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Q: See image

A: