1)lim(1-1/2^2)(1-1/3^2)...(1-1/n^2)

　　首先,我们发现,1-(1/n)^2=(n-1)/n*(n+1)/n

　　所以,(1-1/2^2)(1-1/3^2)...(1-1/n^2)=1/2*3/2*2/3*4/3*...*(n-1)/n*(n+1)/n=(n+1)/(2n).

　　因此,原极限为lim(n+1)/(2n)=1/2

　　2)limn^2[(k/n)-(1/n+1)-(1/n+2)-...-1/(n+k)]

　　首先,我们发现,1/n-1/(n+k)=k/n(n+k)

　　所以,(k/n)-(1/n+1)-(1/n+2)-...-1/(n+k)=1/n(n+1)+2/n(n+2)+...+k/n(n+k)

　　因此,原极限为limn^2*[1/n(n+1)+2/n(n+2)+...+k/n(n+k)]=1+2+...+k=k(k+1)/2