1. Vk +1- Vk = 1 Consider the sequence ak = and the infinite series ak. Which of the following Vk+1+vk k=1 is true? (A) lim ap O and ak converges. k=1 (В) lim ak + 0 and ak converges. k=1 (C) lim ak O and ak diverges. k=1 (D) lim a 7 0 and ak diverges. k=1

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A: All proofs are easily only  a) proved using induction  b) proved using definition c) find using a…

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

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A: To decide whether the sequence  converges and if so, to calculate .

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

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A: Bounded above. Bounded below.

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

Q: True or False: The generating function of the sequence h₁=n+1 is 1/(1-x)². O True False

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Q: 12. Let {P,} be a sequence of points determined as in the figure. Thus |AP,| = 1, | P„Pn + 1 = 2"…

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Q: 2. Determine the limit of the following sequences or state if the sequence diverges. Use the…

A: (i) Given that, an=15n. obtain the limit of an=15n. limn→∞an=a1-r          r&lt;1=11-15=54

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A: This is a problem of sequence and series.

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A: We will find out the required value.