lim(n→+∞)(1/n²+2/n²+3/n²+4/n²+…+(n-1)/n²)=lim(n→+∞)(n²-n)/(2n)=1/2=0.5
lim(n→+∞)[1/(1*2)+1/(2*3)+1/(3*4)+…+1/(n(n+1))]=lim(n→+∞)[1-1/2+1/2-1/3+1/3-1/4+…+1/n-1/(n+1)]=lim(n→+∞)[1-1/(n+1)]=lim(n→+∞)[n/(n+1)]=1