Sn=1/(1*3) + 1/(2*4) + 1/(3*5) + …… + 1/{n(n+2)}
  =(1/2)*{(1-1/3)+(1/2-1/4)+・・・・・・+(1/(n-1)-1/(n+1))+(1/n-1/(n+2))}
  =1+1/2-1/(n+1)-1/(n+2)
  =3/4-1/(n+1)-1/(n+2)
  →3/4-0-0=3/4 (as n→∞)