Lim inf/sup question

1. Jan 8, 2009

transgalactic

i got this example:

http://img405.imageshack.us/img405/2299/64500275qt5.gif [Broken]

i got a sequence of numbers
i cant understand from where they conclude that the limits of every sub sequence is {2,1,0,-1}

there are no sub sequences pointed out
there are no formulas for each sub sequence

how did they came with
that the limits of every sub sequence is {2,1,0,-1}
??

Last edited by a moderator: May 3, 2017
2. Jan 8, 2009

HallsofIvy

Staff Emeritus
The obvious subsequences is {2, 2, 2, 2, ...}, {1, 1, 1, 1, ...}, {0, 0, 0, ...}, and {-1, -1, -1, 0, ...}. Those are the only convergent subsequences.