已知数列{an}满足a1=2,根号下a(n+1)/2an等于n+1/n,求{an}的通项公式?

问题描述:

已知数列{an}满足a1=2,根号下a(n+1)/2an等于n+1/n,求{an}的通项公式?

a(n+1)/2an=n+1/n
所以a(n+1)/an=2(n+1)/n
所以有an=an/a(n-1)·a(n-1)/a(n-2).·a2/a1·a1
=2^(n-1)×4n
=n·2^(n+1)