Use the difference a -a, to show that the given sequence (a,] is strictly increasing or strictly decreasing 3n - 2) d+l - a, = 2. strictly decreasing (3n+2)(3n – 1)' strictly increasing (3n + 2)(3n – 1) 1 strictly decreasing (3n-2)(3n + 2)' strictly increasing (3n- 2(3n + 1)' strictly decreasing (3n- 2)(3n + 1)'

Q: lim 1-26 2 (2 + 3n-4n²) (1-2n + 3n²)

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Q: (a) Give an example of a bounded sequence that diverges.

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Q: Find lim,00 sup(sn) and lim,→0 inf(sn) for the sequence: 82n = (-1)"(n); s2n-1= e7 = et

A: The sequence is S2n=-1nn. Find limn→∞sups2n and limn→∞infs2n: Consider and obtain the limits:…

Q: Which of the following is the generating function for the sequence 5, 5, 5, 5 O A. G(x)=(1-x) 1 O B.…

A: Generating Function: Generating Function is a way to represent an infinite sequence. Consider a…

Q: For the sequence an

A: Given, the sequence      an=2(an-1-2), and a1=1

Q: 5. (i) Determine the sequence gnerated by the following generating functions: (ii) e(1+x) t (1-1)³

A: (5) (i)          Given generating function is t1-t3= t 1-t-3…

Q: (-1)*+1 is The series 2k = 1 2k

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Q: Vn2 + 1 Let (bn)neN be the sequence defined by b, 2n Let e > 0. Derive a value of N (in terms of e)…

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Q: Use the difference anti-an, to show that the given sequence {a} is strictly increasing or strictly…

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Q: Q4: Find the following sequence: Then Make sketch of -3 x(n) = 3n[u(n+3)-u(n-4)] y(n) = x(2n-3)

A: Given below clear explanation

Q: Which of the following is the generating function for the sequence 5, 5, 5, 5,. ? O A. G(x)=(1-x)-1…

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Q: Give the definition of a subsequence of a sequence Xn.

A: the definition of a subsequence of a sequence Xn.

Q: Use the difference an+1 - an to show that the given sequence {a,} is strictly increasing or strictly…

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Q: 7. The sequence (an) = {41} is strictly increasing for increasing n. Show this to be true by +1 (i)…

A: Let {an} be a sequence.Then the sequence is said to be increasing i) if the difference of successive…

Q: The sequence {an} defined by an = (-1)+2 for every integer n ≥ 0 is a solution to the recursive…

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Q: Consider the arithmetic sequence S, where the i-th term of S is defined as follows for positive…

A: Solution; The arithmetic sequence is defined by Si=2+6i-1 We want to prove by induction that the sum…

Q: Find the limit of the sequence: 3n? + 9n + 9 An 2n2 + 2n + 1

A: To find:-

Q: 2.1. Write the first five terms of each of the following sequences. 2n -1 (a) 3n + 2 1-(-1)" (b)…

A: Given: Five sequences. Substitute n=1, 2, 3, 4, 5 to find the first five sequences in the given…

Q: Solve the recurrence defined by a for n ≥ 1. an 3(6^n)-2 3 and : 6an-1 + 5 an =

A: As per the guidelines I am answering only one question at a time. an=6an-1+5, a0=3