设数列{xn},{yn}中,x1=2且x(n+1)=(3xn+1)/(xn+3),yn=(xn-1)/(xn+1)(n∈N*).(1)求证:数列{yn}是等比数列 (2)求yn的极限 (3)求xn的极限
问题描述:
设数列{xn},{yn}中,x1=2且x(n+1)=(3xn+1)/(xn+3),yn=(xn-1)/(xn+1)(n∈N*).
(1)求证:数列{yn}是等比数列 (2)求yn的极限 (3)求xn的极限
答
(1)∵x1=2x(n+1)=(3xn+1)/(xn+3),可以求出X2=7/5并求出Y1=1/3,Y2=1/6∴Y2/Y1=1/2∵yn=(xn-1)/(xn+1)∴yn+1=(X(n+1)-1)/(X(n+1)+1)将 x(n+1)=(3xn+1)/(xn+3)带入上式 得yn+1=(xn-1)/(2xn+2)∴yn+1/yn=(...