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I need to find all partial limits of$a_n=1+\frac{n+1}{n+3}\cos\frac{n\pi}{2} $, how I suppose to know what subsequences exactly to choose?

Thanks a lot!

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What does partial limit mean ? Does it mean all cluster points ? –  Amr Nov 17 '12 at 15:56
    
@Amr I mean limits of subsequences –  Tina Nov 17 '12 at 16:09
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Hint: $\cos(\frac{n\pi}{2})=0$ for odd n, $cos(\frac{n\pi}{2})=-1$ for $n=2 (mod4) $, $cos(\frac{n\pi}{2})=1$ for $n=0 (mod 4)$

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Why do you choose mode 4, not 5,6 or any else number why 4?Thanks. –  Tina Nov 17 '12 at 16:14
    
OK. I will put this in my answer. –  Amr Nov 17 '12 at 16:17
    
@ Amr Thanks, waiting for your explain –  Tina Nov 18 '12 at 8:19
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