Prove that the sequence {n³ + 1/n³} is a cauchy sequence.

Q: For the sequence an = n +1' its first term is its second term is its third term is its fourth term…

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Q: Find the generating function for the sequence 1,−2,4,−8,16,….

A: The general expansion of the binomial (1-x)-1 will be, (1-x)-1=1+x+x2+x3+….

Q: Use polynomial fitting to find a closed formula for the sequence (an)n 2 1: 4,11, 20, 31, 44,..

A: Given Sentence is 4,11,20,31,44......We can see that       11-4 =7                        }⇒9-7=2…

Q: Find the limit of the sequence: 3n² + 3n+6 ап 7n² + 7n +9

A: Step 1: The limit of a sequence is the value that the terms of the sequence approach as the index n…

Q: Express the sum 3 + 5 + 7+ ... + (2k-1) using E-notation.

A: The given sum is 3+5+7+…+2k-1. Express the sum 3+5+7+…+2k-1 using ∑ notation as follows.

Q: Find the generating function for the finite sequence 2, 2,2, 2, 2, 2.

A: Step 1: Consider the provided question, Given, the finite sequence 2, 2, 2, 2, 2, 2.

Q: The greatest lower bound for the sequence {2, 4, 8, 16, 32, 64, . } is

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Q: Find an  for the sequence 1/1 -22/2x1 +33/3x2x1 - 44/4x3x2x1, +...

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Q: 2. If a 1 and an+1 for each n> 1. Use the mathematical induction to show the sequence (an) is…

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Q: determine the closed formula that generates the sequence 1,2,4,8,16,32

A: The given sequence in the question is:

Q: Determine whether the sequence an= 5n+3 Justify your answer. is monotonic. Is it bounded?

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

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

Q: Calculate an for the sequence 2/(12+1) +1/(22+1) +2/(32+1) +1/(42+1) +.

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Q: Indicate the generating function of the sequence defined by ak = = 4ak-1 +5

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Q: Find the closed form of the generating function for the sequence 2,4, 8, 16, 32, ...

A: Generating Function: Let a0, a1, a2, a3, a4, .....be a sequence of real numbers denoted as an Then a…

Q: Find ai for the sequence with generating function, 1-x 1 x x

A: Simplify the generating function.

Q: Can you use polynomial fitting to find the formula for the nth term of the sequence 4, 7, 11, 18,…

A: No. The sequence of differences is the same as the original sequence so no differences will be…

Q: Use polynomial fitting to find the forumla for the nth term of the sequence (an) n>and equal to 0…

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Q: Find the generating function for the finite sequence 1, 4,16, 64, 256.

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Q: Use polynomial fitting to find the formula for the nth term of the sequence (an)n>0 which starts, un…

A: First check successive difference: where two successive difference is constant that is the degree of…

Q: Find the first 10 terms of the sequence An 2n + 3. its 9th term is its 10th term is

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Q: Define a sequenceK1 = 1, K2 5, and KN KN-1 + KN-2. %3D Determine K4 K5 = II

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