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 Math Emeritus Sci Advisor Thanks PF Gold P: 39,339 The sequence $a_n= (-1)^n n$ does NOT converge, even in the sense of "to $-\infty$" and "to $-\infty$". However, it has two subsequences to $diverge$ to those values: $a_n$, for n even, diverges to $+\infty$ while $a_n$, for n odd, diverges to $-\infty$.