lim[(1-1/4)(1-1/9)...(1-1/(n+1)^2]=lim(1/2*3/2*2/3*4/3*3/4*5/4...*n/(n+1)*(n+2)/(n+1)=lim(1/2*2/3*3/4*...*n/(n+1)*3/2*4/3*5/4*...(n+2)/(n+1)=lim(1/(n+1)*(n+2)/2)=lim(n+2)/(2*(n+1))=1/2