What is an alternating sequence?

1 Answer
Oct 29, 2015

See explanation

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:

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

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

  3. #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