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HallsofIvy
HallsofIvy is offline
#6
Mar16-12, 07:41 AM
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The sequence [itex]a_n= (-1)^n n[/itex] does NOT converge, even in the sense of "to [itex]-\infty[/itex]" and "to [itex]-\infty[/itex]". However, it has two subsequences to [itex]diverge[/itex] to those values: [itex]a_n[/itex], for n even, diverges to [itex]+\infty[/itex] while [itex]a_n[/itex], for n odd, diverges to [itex]-\infty[/itex].