title: 数学难题之3,求救要有步骤 
desc: 要有步骤
answer: Sn=a1+a2+a3+......+an=n^*an
   S(n-1)=a1+a2+a3+......+a(n-1)=(n-1)^*a(n-1)
  
  an=Sn-S(n-1)=n^*an-(n-1)^*a(n-1)
  
  (n-1)^*a(n-1)=(n+1)(n-1)an
  an/a(n-1)=(n-1)/(n+1)
  a2/a1=1/3
  a3/a2=2/4
  a4/a3=3/5
  a5/a4=4/6
  .....
  a(n-3)/a(n-4)=(n-4)/(n-2)
  a(n-2)/a(n-3)=(n-3)/(n-1)
  a(n-1)/a(n-2)=(n-2)/n
  an/a(n-1)=(n-1)/(n+1)
  
  an/a1=(a2/a1)*(a3/a2)*(a4/a3).....an/a(n-1)
       =2/[n*(n+1)]
  a1=1/2
  an=1/[n*(n+1)]
    =[1/n]-[1/(n+1)]
  Sn=[1/1]-[1/2]+[1/2]-[1/3]+[1/3]-[1/4]+....+[1/n]-[1/(n+1)]
    =1-1/(n+1)
  =n/(n+1)
  
  