求通项式已知bn+1=bn^2+bn数列{bn}已知b1=1满足bn+1=bn^2+bn(注：n为右下标）急已{bn}满足bn+1=bn^2+bn记Cn=1/1+bnSk为数列{Cn}前K项和,Tk为数列{Cn}的前K项积,求证:T1/S1+T1+T2/S2+T2……Tn/Sn+Tn

Question

求通项式 已知bn+1=bn^2+bn
数列{bn} 已知b1=1满足bn+1=bn^2+bn(注：n为右下标）急 已 {bn} 满足bn+1=bn^2+bn 记 Cn=1/1+bn Sk 为数列{Cn}前K项和,Tk为数列{Cn}的前K 项积,求证:T1/S1+T1+T2/S2+T2……Tn/Sn+Tn

Answer 1

1/b[n+1]=1/(b[n](b[n]+1))=1/b[n]-1/(b[n]+1)
1/(b[n]+1)=1/b[n]-1/b[n+1]