Find the generating function of the sequence {a}>o defined by ifk mod 3 = 2 if k mod 3 € 2 ak 4² 1-³ 4 1-2³ 4, 0, None of these. 4² 1-20 4

Q: (4) Determine the generating function for the sequence ho, h1,..., where hn = #((a1, a2, a3, a4) |…

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Q: 14. Let do, d1, d2, .. be defined by the formula d, = 3" – 2" for all integers n > 0. Show that this…

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Q: Prove by induction that the sun of the first n terms of the sequence 17,20,23,26 is given by the…

A: The given sequence is .The sum of the first  terms of the sequence is .The aim is to prove the sum…

Q: -, 1-, 3, 6, 12, 24 ...; find the 10th term and the sum of the first 10 terms.

A: The solution is given as

Q: Suppose that b₁ D₂ Dzi is a sequence defined as follows. bk = 5b ³|k/21] b₁ = 0 and b₂ = 3 True or…

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Q: Using the generating function to determine the number of ways  18 identical balloons can be given…

A: Given that 18 identical balloons can be given to 3 children such that each child receives at least 5…

Q: A sequence is said to be decreasing sequence if Vn >1 2n.a O n+1 'n²³n+1·bO n+ n+1dO n+ 1

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A: Given recurrence relation, xn=5xn-1-6xn-2                  ...(1) And x1=1 , x2=5

Q: 1. Find he fifth term of the that has an nth term of (-1)! sequence - 730 D 120 (E)these noneof a…

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Q: For an integer n > 1, how many decimal stings of length n begin or end with an even digit? 5(10)"-1…

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Q: 1. Consider a sequence {an} defined by recurrence: a1 =1, and an = 2an-1+5 for n 2. Prove using…

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Q: Show for all integers n> 1 that 7 I (3ªn+l – 5²n-1 ).

A: a) Prove 734n+1-52n-1 for all integers n≥1 by mathematical induction as follows. Basis step: For…

Q: Which one of the sequences below is divergent? 2n? 3n + 17 2n 3n + 5J 2n n +n +1 D {2-} D

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Q: 4. Define the sequence an by a, = 1, a, = 33, and an = 3an-1+ 10an-2 for n 2 3. Prove that an = 5" –…

A: Concept used :- we use mathematical induction to solve the given question.

Q: The sequence with a₁ = 2 and recurrence relation an = an−1 + (2n + 5) generates these first few…

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Q: 5. Suppose b₁,b2, b3, ... is a sequence defined as follows: b₁ = 4, b₂ = 12 bk = bk-1 + bk-2 for all…

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Q: show that if a₁, a2,..., a5 is a sequence of 5 terms, then 5 Па = 0 i=1 iff at least one term of the…

A: Let the sequence of five terms be as follows:To Find:Show that  iff at least one term of the…

Q: g) Determine the product of Factorial of 5 and Fibonacci of 5 using the recursive function as…

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Q: Find an explicit formula for a sequence ao, a1, a2, a3, . . . that satisfies — 24. (Hint: ат Cr" +…

A: To find the explicit formula for a sequence given using recurrence relation find the characteristic…

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: Find an explicit formula in terms of n for a sequence bo, b₁,b₂, 10bk - 2 for each integer k ≥ 2 bk…

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Q: The sequence {a} begins with 2, 1,-1, -2, -1, 1, 2, ... n From the list below select a recurrence…

A: Option (B) is wrong as the initial conditions a0 = 3 and a1 = -1 are not true.    Option (C) is…

Q: 2 13. Write the sum 2++ in sigma notation in 25 three ways: with a starting value of (a) k = 1, (b)…

A: a) The series can be written in compact form using sigma notation Here the terms are written…

Q: When the terms are arranged in descending powers of z, determine the middle 8 3 term in the…

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Q: b. Suppose that {a} is a sequence of real numbers defined recursively by a₁ = 1, a₂ = 2, and an+2 =…

A: note :Since you have posted multiple questions, we will provide the solution only to the first…

Q: Given is a sequence bn defined in recursive form 1 A * = (-+ ^^) bn - n-1 2 bn-1 for a given A> 0.…

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Q: The sequence with a₁ = 1 and recurrence relation an =an-1 + (2n + 5) generates these first few…

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Q: inf{a,b, : n e N} > (inf{a, : n € N}) × (inf{b, : n E N}). (1) Does the inequality (1) continue to…

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Q: 10. a. Write the first 4 terms of the sequence defined by an = (-1)n n!/3n; n20 C. b. For Fibonacci…

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Q: Determine how many terms of (-1)*+lgk must be summed to be sure that the remainder term k! k=1 is…

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Q: Find the number of ways that the numbers 1, 2, ..., 12 can be arranged in a sequence…

A: Observed that each sequence contain 1st 6 elements in descending order and remaining 6 elements in…

Q: Let an = 1 for n = 1, 2, 3, ... . Write out the the first three terms of the following sequences. 3n…

A: Given  To find (a)  then find (b)  then find (c)  then find (d)  then find

Q: Select each expression that has a sum of 4 4/12 3 1/5 + 1 3/7 1 11/12 + 2 1/4 1 3/6 + 1 1/2 + 1…

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Q: 8. Suppose ao, a1, a2, ... is a sequence such that ao = a₁ = 1 and, for n ≥ 1, an+1 = n(an + an-1).…

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Q: 3.4. A sequence s,, S2, S3, ... is defined recursively as follows: Sk = 5Sk-1 + (Sk-2)2 for all…

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Q: Let a and b be positive numbers with a>b. Let a1 be their arithmetic mean and b1 their geometric…

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