设数列{an}满足a1=0,1/(1-an+1)-1/(1-an)=1设数列{an}满足a1=0,1/(1-an+1)-1/(1-an)=1(1)求{an}的通项公式(2)设bn=(1-(an+1)1/2)/(n)1/2,记Sn=b1+b2+…+bn,证明Sn<1

问题描述:

设数列{an}满足a1=0,1/(1-an+1)-1/(1-an)=1
设数列{an}满足a1=0,1/(1-an+1)-1/(1-an)=1
(1)求{an}的通项公式
(2)设bn=(1-(an+11/2)/(n)1/2,记Sn=b1+b2+…+bn,证明Sn<1