EXERCISE 7: Sequence: The first term of a sequence is a1 = sin(1). The next terms are: a2 = min{a1,sin(2)} (the smallest of a1 and sin 2), az = min{a2, sin(3)} (the smallest of az and sin 3),... an+1 = min{an, sin(n + 1)} (the smallest of an and sin(n +1)). Is this sequence {an} converging or diverging?

Q: {1- The sequence is en (i) 0 (ii) 1 (iii) None of these

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Q: If z1=1-i,z2=-2+4i then evaluate: modulus of (z1+z2+1)/(z1-z2+i)

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Q: 5. The sequence -1, 1, -1, 1.....is (а) A.P (b) G.P (c) Н.Р (d) None

A: since u have asked multiple questions in a single request , so we will be answering only first…

Q: 1+ x Σ Aa" (1 – 2)? n=0

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Q: inf{a,bn :n e N} > (inf{an : n e N}) × (inf{b, : n € N}). (1) Can the inequality in (1) be strict?…

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Q: Prove: For any positive integer n, x™1 - yl = (x- y) xy' (You may use the laws | of exponent in your…

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Q: Determine L{"e3r cos(t-7)dr} 0 Select one: (8+3)(82+1) 8 (8+3)(82-1) 8 (8-3)(82+1) 8 (8-3)(82-1)

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Q: Question 10 1 1 1 1 2 4 8 16 32 Consider a sequence whose first five terms are Which function can be…

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Q: Consider the quadratic function : C→C defined by f(3) = ² + i. (a) What is the long term behavior…

A: Given : A quadratic equation f:ℂ→ℂ defined by f(z)=z2+i. To find : (a) The long term behavior for…

Q: Determine if the sequence is increasing, decreasing, not monotonic, bounded below, bounded above…

A: (a)…

Q: 2. tan 4 0 + tan ² 0 = sec4 0 – sec ² 0

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Q: Prove that this sequence is monotonic: an = cot-n

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Q: Suppose that (0) is a null sequence with only nonzero terms. Calculate lim 818 0 Submit Question sin…

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Q: (a) Write out the first four terms of the sequence {1+ (-1)"}, starting with n = 0. (b) Write out…

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Q: 3. Determine whether the sequence is monotonic. Prove you are correct. (a) {n²} {} e {1+} (d) {} 1…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

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

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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: Evaluate 1) Sin ¹ (1 a) cos`' (-1) 3) cos( tan`¹ (13 Sin (1/ กาก

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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: Let F, F₁, F2, ... denote the Fibonacci sequence. Find an expression for (Fk+ 1)² – (FK)² a…

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Q: (1-x) (1+x) Find the coefficient of x" in the expansion of

A: In this problem, we have to use the expansion of (1+x)-2 and multiply the brackets to obtain the…

Q: Only use epsilon defination , Let be a sequence of positive terms such that pn-> p show that…

A: We apply only Epsilone defination.

Q: .Find a sequence that diverges, but doesn't diverge to infieity (a) an = n+1 (b) bn %3D Vn +1 (c) Cn…

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Q: Find the sequence corresponding to generating function 1/(1-az).

A: We will find out the required sequence.

Q: Number 3

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Q: Rewrite -ln(3)+ln(4)-ln(5)+...+ln(20) using summation notation.

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Q: Establish the 1dentity COSLIT-e)=- čos O Write down the Sequence of Steps that verify iolentity the

A: Given- cosπ-θ=cosθ To Find- The sequence of the steps that verify the above identity. Identity Used-…

Q: Let (a_n)be the sequence defined by the recursive relation a_n=na_(n−1), with initial term a0=1.…

A: Given that:  an=nan-1               a0=1

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.