I wonder if any of you are smart enough to come up with ONE test that determines

Question

I wonder if any of you are smart enough to come up with ONE test that determines convergence/divergence for ANY series that can be performed on a TI-84 (as opposed to the 9 or so different tests and conditions that one currently has to memorize and use depending on the type of series)

Explanation / Answer

Alphabetical Listing of Convergence Tests Absolute Convergence If the series sum (1..inf) |an| converges, then the series sum (1..inf) an also converges. Alternating Series Test If for all n, an is positive, non-increasing (i.e. 0 1, then the series converges. If 0

1, then the series sum (1..inf) an diverges. If L = 1, then the test in inconclusive. Root Test Let L = lim (n -- > inf) | an |1/n. If L < 1, then the series sum (1..inf) an converges. If L > 1, then the series sum (1..inf) an diverges. If L = 1, then the test in inconclusive. Taylor Series Convergence If f has derivatives of all orders in an interval I centered at c, then the Taylor series converges as indicated: sum (0..inf) (1/n!) f(n)(c) (x - c)n = f(x) if and only if lim (n-->inf) RN = 0 for all x in I. The remainder RN = S - SN of the Taylor series (where S is the exact sum of the infinite series and SN is the sum of the first N terms of the series) is equal to (1/(n+1)!) f(n+1)(z) (x - c)n+1, where z is some constant between x and c. for divergence test goto this link http://en.wikipedia.org/wiki/Harmonic_series_%28mathematics%29#Paradoxes

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