2. Suppose the sequence {sn} satisfies |8n+1 = 8n| ≤ 7/²2 for all n E N. Prove that {sn} converges.

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Q: Prove {52 + 11/n} n=1 to infinity converges to 52 using the definition of a convergent sequence.

A: Prove {52 + 11/n} n=1 to infinity converges to 52 using the definition of a convergent sequence.

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A: Statement : Every bounded sequence of real numbers has a convergent subsequence.

Q: 43) Suppose that an > 0 for all n and that n=1 anbn necessarily converge? ∞ Σa an converges. Suppose…

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Q: 2. Suppose the sequence {sn} satisfies Sn+ 1 - Sn ≤ -1/24 n² For all ne N. Prove that {sn}…

A: Given that the sequence  satisfies .The objective is to find for all ,  converges.

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Q: 1. Prove that the sequence converges to . 2n+1

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Q: 5. Use the definition of convergence to prove that the sequence (sn) diverges where Sn = √n.

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Q: Determine whether it is uniformly convergent £r20 x2+k2

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A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…