在数列{an}中,a1=1,且对任意K∈N*,a(2k-1),a(2k),a(2k+1)成等比数列,其公比根号下[（k+1）/k],则...在数列{an}中,a1=1,且对任意K∈N*,a(2k-1),a(2k),a(2k+1)成等比数列,其公比根号下[（k+1）/k],则a2011的值为（

Question

在数列{an}中,a1=1,且对任意K∈N*,a(2k-1),a(2k),a(2k+1)成等比数列,其公比 根号下[（k+1）/k],则...
在数列{an}中,a1=1,且对任意K∈N*,a(2k-1),a(2k),a(2k+1)成等比数列,其公比 根号下[（k+1）/k],则a2011的值为（ ）
感激不尽

Answer 1

a(2k+1)/a(2k-1)=(k+1)/k
a(2k-1)/a(2k-3)=k/(k-1)...
a3/a1=2/1
左右累乘
a(2k+1)/a1=[2×3×...×(k+1)]/(1×2×3×...×k)=k+1
a(2k+1)=a1(k+1)=k+1
(2011-1)/2=1005 k=1005
a2011=1005+1=1006