10/ Give a recursive definition of the sequence {a}, n = 1,2,3,...if an = 6n+2 11/ Find the least integer n such that f(x) is 0(x" ) for each of these functions. a) f(x) = 2x + (logx) ¹0 b) f(x) = (x¹+5log x)/(x+10)

Q: Please give an example of a sequence (an) that has: (a) an(k) = (1/k) as a subsequence where n(k)=…

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Q: bn Уп? + 6п — п,

A: Given that the sequence bn=n2+6n-n where n∈ℕ and ℕ is the set of natural numbers. We have to…

Q: A sequence {a„}1 satisfies a1 = 1, a2 = 1 and 6 an = max {an-1, an-2} – min {an-1, an-2} for n > 3.…

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Q: 6n2 – 7n An 2n2 + 9

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Q: (6) Let {an} be the sequence defined by an+1 = √6an 2, a₁ = 1. Show that {an} is converger and find…

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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: Let U be the set of first 10 even positive integers, A is set of multiples of 3 in U and B is set of…

A: It is given that; U = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {3, 6, 9} B = {4, 8}

Q: 1. The field mouse population in a certain area is known to naturally increase at a rate of 50% per…

A: The population of mice is increasing at a rate of 50% per month. The mice killed and eat each month…

Q: Let (an) be the sequence defined recursively by a₁ = An = √3. √2an-1 +3, Prove that (an) is…

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Q: 2. Let an be the sequence defined inductively by a₁ = 2 and an+1 == 1/2 (a₁ + ²2² ). an (a) Prove by…

A: a. By induction, we can conclude that an € [1,2] for all  n € N.b. It is proven that an2 >= for…

Q: 5. If a = (1+ 1)", then which of the following statement is true for the nth term of the sequence…

A: The solution is given as follows :

Q: al = /3 , a2 = V 3- V3 , V 3 - V 3+ v3+ .. + V3 ....

A: We have to find the limit of the sequence…

Q: 8. Consider the sequence {an} such that an+1 = -3 – 2an. Then lim an = -1.

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Q: Prove that sequence {an}= {(-1)n} does not have a limit.

A: According to the given information it is required to show that {an}= {(-1)n} has no limit.

Q: If {b,}-1 is a bounded sequence and lim,→∞ An = lim,-+∞ anbn? Justify. 0, what can you say about

A: Given that  bn is bounded sequence, so, by definition of bounded sequence  ∃B>0 such that bn<B…

Q: Write out the first five terms of the sequence (n+4)² determine whether the sequence converges, and…

A: Given limn→∞-1n-1n+42

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

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Q: 2n + 3 Which of the following is true about the sequence (a,) where a, = 5n + 4 (a) lim a, = +oo (b)…

A: Given that; an=2n+35n+4

Q: 1 Let xn=G, 2+-), nEN be a sequence in R?, then lim x, .A (0,2) .B [0,2] .C (2,3) .D (0,2]

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Q: 10. Let {xn} be a sequence of real numbers. What does the limsup of this sequence mean?

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Q: Justify each step in the following proof sequence of (Ax)P(x) ^ (Vx)(P(x) → Q(x)) → Ax)Q(x) 1.…

A: Given: ∃xPx∧∀xPx→Qx→∃xQx. We have to justify the steps of the proof: 1. ∃xPx 2. ∀xPx→Qx 3. Pa 4.…

Q: Find a sequence of real numbers {a;} such that lim a, does not n-00 xist, but it has 3 subsequential…

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Q: Indicate a general rule for the nth term of the sequence when a, = 2 and r = a, = (/2)(5y* a, =…

A: Given query is to find the nth term of the sequence.

Q: 1. Let a, = 1 and an+1 = 1+ 1+an (a) Find the first six terms of the sequence {an}. (b) Prove that…

A: As you asked multiple sub parts so I answered 1st three subpart.

Q: Please give an cxample of a sequence (a,) such that: (a) (an) is not bounded above. (b) (an) is not…

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