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[Axiom-developer] [#234 limit((-1/2)^n, n=%plusInfinity)] An answer to m

From: unknown
Subject: [Axiom-developer] [#234 limit((-1/2)^n, n=%plusInfinity)] An answer to my question, from William Sit.
Date: Sun, 13 Nov 2005 11:27:39 -0600

William Sit <address@hidden> responded via emai, and wrote, in part:

Mathematically, the limit is 2 since (-2/%pi) has absolute value less than 1,
and hence (-2/%pi)^n converges to 0. So TI-89t is correct and Axiom is wrong.

In the second case, TI-89t is wrong to say that limit (-1)^n is -1. The limit 
does not exist
because the sequence (-1)^n oscillates between 1 and -1. There is no number L
(the assumed limit) such that given any epsilon > 0, there is a natural number N
such that |(-1)^n - L| < epsilon for all n > N.
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