# Partial limits of sequence of trigonometric functions

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

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 $n=0 (mod 4)$