已知数列(An)中,A1=1/3,AnAn-1=An-1-An(n>=2),数列Bn满足Bn=1/An,求数列Bn的通项公式需要详_数学解答

已知数列(An)中,A1=1/3,AnAn-1=An-1-An(n>=2),数列Bn满足Bn=1/An,求数列Bn的通项公式
需要详细的步骤

人气：149 ℃　时间：2019-09-17 13:26:25

解答

AnAn-1=An-1-AnAnAn-1+An=An-1An=An-1/(A(n-1)+1) n>=2 A1=1/3A2=A1/(A1+1) =1/3/(1/3+1)=1/4A3=A2/(A2+1)=A1/(A1+1) / (A1/(A1+1)+1)=A1/(A1+A1+1)=A1/(2A1+1)=1/3/(2/3+1) =1/5A4=A3/(A3+1)=A1/(2A1+1) / ( A1/(2A...