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Pre-Calculus Practice Problem 232

Pre-Calculus Practice Problem 232 - rational function...

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Unit 7, Activity 4, Infinite Sequences and Convergence Part I with Answers Blackline Masters, Advanced Math – Pre-Calculus Page 230 Louisiana Comprehensive Curriculum, Revised 2008 My Opinion My Opinion Statement If you disagree why? Lessons Learned 1. Sequences whose nth term formula is geometric: t ar n n = 1 are convergent. It depends on the value of r . If -1 < r < 1 then the sequence is convergent. If r > 1 or r < -1 then the sequence is divergent. 2. Arithmetic sequences are always divergent. Arithmetic sequences have nth term formulas that are linear. The end-behavior for a linear function is ±∞ . 3. All sequences whose nth term uses a
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Unformatted text preview: rational function formula are convergent. Only those sequences whose nth term formula has a horizontal asymptote y = k, k a real number, will converge. 4. . All sequences whose nth term formula is a composition f(g(x)) will converge only if both f and g are convergent. Not necessarily. If f g x k ( ( )) , → k a real number, as n increases without bound, then the sequence is convergent. 5. All sequences whose nth term is a periodic function are divergent. Not necessarily. See the answer above. If the periodic function is f of f ( g ( x )) and g ( x ) converges to a real number, then the sequence is convergent....
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