A sequence {a^n} of real numbers is defined recursively by a_1=2 for n ≥ 2, a_n=(2+1∙a_1^2+2∙a_2^2+⋯+(n-1) a_(n-1)^2)/n Determine a_(2,) a_3, and a_4. Show all work. Clearly, a_n is a rational number for each n ϵ N. Based on the information in a), however, what conjecture does this suggest?

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A: This is a problem of Sequence.

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A: a1=14a2=-85a3=276a4=-647

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A: To determine the value of the limit.

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A: We disprove the result by giving a counter example.

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A: The answer is in step 2.

Q: (-1)"n An n +1

A: We have to evaluate the limit of the sequence an=-1nnn+1.

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A: Given: So,              a2=2a1=20=1a3=2a2=21=2a4=2a3=22=4a5=2a4=24=16a6=2a5=216=65536

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Q: Write an explicit formula for the sequence: 1 1 1 1 1 an 2 - — 6' 7 9 8 2 — 9 9 1 10 9 -.}

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