What is an alternating sequence? + Example

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