I need to find all partial limits of$a_n=1+\frac{n+1}{n+3}\cos\frac{n\pi}{2} $, how I suppose to know what subsequences exactly to choose?
Thanks a lot!
I need to find all partial limits of$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!
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 $n=0 (mod 4)$