What is an alternating sequence?

Answer 1

See explanation

Alternating sequence is a sequence, whose term change sign (i.e. if a term #a_n# is positive then #a_{n+1}# is negative and vice versa)

Examples:

#a_n=(-1/2)^n# This sequence would have terms: #-1/2;1/4;-1/8;1/16;...#

#b_n=(-1)^n#. This sequence would have terms: #-1;1;-1;1;...#

#c_n=(-1)^n*n# This sequence would have terms: #-1;2;-3;4;...#

Note that such terms can be either convergent: #lim_{n->oo}a_n=0#, or divergent: #lim_{n->oo}b_n# does not exist

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Answer 2

Paisley Johnson

An alternating sequence is a sequence of numbers in which the sign (positive or negative) alternates between consecutive terms. In other words, the terms of the sequence alternate between being greater than and less than zero. For example, the sequence (1, -2, 3, -4, 5, -6, \ldots) is an alternating sequence because the signs alternate between positive and negative.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.