Use the difference an+1 - an to show that the given sequence {a,} is strictly increasing or strictly decreasing. { 71 4n-3Jn=1 Antl - an = 3 strictly decreasing (4n + 3)(4n – 1)' 3 strictly increasing (4n + 3)(4n – 1)' strictly increasing (4n 3)(4n + 1) 3 strictly decreasing (4n 3)(4n + 1) strictly decreasing (4n 3)(4n+3)

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

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Q: 11. (6 points) A sequence is given by the recursive definition bn = 4bn-1, bo = 3. a) Find b₁,b₂,…

A: The objective of the question is to find the values of b_1, b_2, b_3 and a general formula for b_n,…

Q: II(2) b, = II(2i + 1). an = e i=1 i=1

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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: The sequence {bn}∞n=1 is defined as b1 = 5 , b2= 13, bn = 5 bn −1 − 6 bn −2 for n ≥ 3. Prove bn…

A: 8 Given that the sequence bnn=1∞ is defined as b1=5, b2=13 and bn=5bn−1−6bn−2. We have to prove that…

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: Rewrite x-x3/3+x5/5-x7/7 using summation notation.

A: We have to find the summation

Q: 4. Consider the sequence 8 1 {2(k+3 (2(k+3)) k=1 rewrite the sequence from j-5

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Q: Find the sum : [00 En = n=0 (-1)" πT 2r q" (2n)!

A: We have given a series ,  ∑n=0∞ (-1)n π2n9n 2n! We need to find the sum of series ,  ∑n=0∞ (-1)n…

Q: 4. Let n >1 be an integer. Consider the following expression 3 (3* – 212 + 2) – 2 (3* – 3k2 + 2) k=1…

A: Let's find.

Q: Liminf of the sequence is an = √2n(√2n +4 | 3 + 1/1/0 n √2n) n is a prime number n is not a prime…

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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: The generating function of the sequence 4,4,4,4,4 is

A: # To find generating function of sequence  4,4,4,4,4,4 ??

Q: an = (-1)", bn Cn = n² dn= n (a) For each sequence, give an example of a monotone subsequence. 6n +…

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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: Use the formula for the sum of the first n integers and/or the formula for the sum of a geometric…

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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: a. the sequence is given by an=1/(n^7/6)      lim n→∞ an=  b.  the sequence is given by…

A: We need to solve separately a. the sequence is given by an=1/(n^7/6)      lim n→∞ an=  b.  the…

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: Let the sequence 9n be recursively defined by go = 0, 91 = 1, 9n = In-1 +29n-2 for n ≥ 2. Show that…

A: Given recurrence relation: