Prove that the sequence is increasing.

Q: true or false: if the sequence [a sub(n)] is monotone decreasing, then [a sub(n)] must converge

A: Follow next step

Q: A convergent sequence is bounded. A True B False

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Q: Let Fn be Fibonacci sequence. Prove that:

A: By the definition of the Fibonacci sequence, Fn+2=Fn+1+Fn and the Fibonacci sequence is satisfied…

Q: Show that the sequence defined by  a sub 1= 1  and  a sub n + 1 = 3 - (1/ a sub n) is increasing and…

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Q: 1 Prove that if a sequence {a„} converges to a, then the sequence {[an]} converges to |a|. Find…

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

Q: If the sequence {a}, is convergent, then the sequence {x} defined by a₁+as+as++an-stan is also…

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Q: The greatest lower bound for the sequence {0.1,0.01,0.001, 0.0001, ...} is

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Q: Prove that if a sequence  {an} converges, it must be bounded. Is the converse true as well

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Q: Decide whether or not the infinite sequence is a cauchy sequence. If it is not a cauchy sequence,…

A: The given sequence   is Cauchy sequence. Here,                        Let  p be any natural number.

Q: Prove that each convergent sequence of reals is bounded.

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Q: If (an) is a sequence converging to L, prove that (an)=1 converges to L.

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Q: Does this mean the sequence is always convergent?

A: We can take limit of the sequence.  limn→∞an=limn→∞-1n-1nn+n

Q: Suppose that the sequence {an} converges to a, where 0 < a < 1. Prove that the sequence {a}…

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Q: Find an explicit formula for the sequence of the form a1, a2, a3, . . . with the initial terms…

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

A: To know weather two function converge or not take difference of them and put limit to infinite. If…

Q: Every convergent sequence is bounded. O True O False

A: Every convergent sequence is a bounded sequence, that is the set {xn : n ∈ N} is bounded. Remark :…

Q: If (Xn) is a monotone sequence, then (x,) converges O False O True

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Q: Prove that a convergent monotonic sequence is bounded.

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Q: A sequence that does not have any convergent subsequence

A: We find a sequence that does not have any convergent subsequence.

Q: Show that a convergent sequence is bounded both up and down.

A: Show that a convergent sequence is bounded both up and down.

Q: Assume that the recursively defined sequence converges and find its limit. a, = - 12, an - 1 = /24 +…

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Q: Prove that there is no sequence of real numbers whose set of accumulation points is exactly Q

A: Answer given below.

Q: Let (an) be an increasing sequence of real numbers bounded from above and (bn) be a decreasing…

A: Given an is an increasing sequence of real numbers bounded above and bn  is a decreasing sequence.…

Q: Determine whether ∞∑n=1√n / 2n2+n+5 is convergent.

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Q: b. Does the sequence an n converge or diverge? Justi

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Q: Show that any sequence of positive real numbers either has a subsequence that converges, or else a…

A: We have to show that any sequence of positive real numbers either has a subsequence that converges,…

Q: Show that a sequence in R" converges if and only if the i-th coordinates of the sequence converge in…

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