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Ratio test

AP.CALC: LIM‑7 (EU), LIM‑7.A (LO), LIM‑7.A.11 (EK)

Problem

a, start subscript, n, end subscript, equals, start fraction, n, minus, 2, divided by, left parenthesis, n, plus, 1, right parenthesis, !, end fraction
1) Find limit, start subscript, n, \to, infinity, end subscript, open vertical bar, start fraction, a, start subscript, n, plus, 1, end subscript, divided by, a, start subscript, n, end subscript, end fraction, close vertical bar.
limit, start subscript, n, \to, infinity, end subscript, open vertical bar, start fraction, a, start subscript, n, plus, 1, end subscript, divided by, a, start subscript, n, end subscript, end fraction, close vertical bar, equals
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0, point, 75
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
2) Based on your answer, what does the ratio test say about S, equals, sum, start subscript, n, equals, 1, end subscript, start superscript, infinity, end superscript, a, start subscript, n, end subscript?
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