Question 579911
{{{a[1]= cos(pi/2)=0}}}, {{{a[2]= cos(2*pi/2)=cos(pi)=-1}}}, {{{a[3]= cos(3*pi/2) =0}}}, {{{a[4]= cos(4*pi/2)=cos(2*pi)=1}}}, and it repeats from then on because cosine is periodic with a period of {{{2*pi}}}, so {{{a[5]=a[1]=0}}}, {{{a[6]=a[2]=-1}}} and so on. In general {{{a[n+4]=a[n]}}}
{{{-1<a[n]=cos(n*pi/2) <=1}}}, but {{{a[n]}}} does not converge. It just keeps flip-flopping between 1 and -1, hitting 0 in between. There is no limit.