Question 6: Consider the following statement: let (a,)n21 be a convergent real sequence satisfying a, >0 for all n 2 1. Then (bn)n21 converges, where a1 +..+ an b Is the statement true? If so give a proof, if not provide a counterexample.

Q: 1 The sequence converges to - 2 /n² – 1 – /n² + n 20 Select one: True O False

A: The sequence 1n2-1-n2+n   converges to -2    we have to check it is true or false.

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A: Given

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A:

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A: If you like the solution then please give it a thumbs up.... The Answer is:           Result :…

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A: Suppose {an} converges to a. Prove that an converges to a. Also, check the converse is true.

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

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A:

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Q: Find the conditions necessary for this sequence to be Cauchy. Хп xn+1 = axn+b 1 + xn

A: For the sequence (Xn)(Xn​) defined by the recurrence relation to be Cauchy, the condition necessary…

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A:

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A: The convergence of the series can be checked by applying the limits to ∞. The convergence of the…

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A:

Q: 1. Prove that the sequence {4+} converges to 4.

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A: We have to check wheather it is true or not

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A:

Q: 10. Which of the following statements is /are not true? I. Every convergent sequence is Cauchy. II.…

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Q: 9. Find the explicit formula for a sequence satisfying а, %3D10а,, + 25а, _,n22 n-1 а, %3D 3, а,…

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Q: Consider the sequence 4.8, 7.68, 12.288,... Note that 4.8; is t(1), not t(0). a) Is this sequence…

A: the sequence given to us is  4.8, 7.68, 12.288, ...

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Q: What does Ek=1 converge to? Ak+11 k+12.

A:

Q: Which one of the following sequences does diverge to infinity? O a. 4n= (-1)"(1-) Inn O b. an In 2n…

A: We have to check