已知数列{an}满足a1=1,An+1=an/1+2an(n属于N*) 问若若a1a2+a2a3+……+anan+1>16/33,求n取值范围
已知数列{an}满足A1=1,An+1=An/1+Aan(n属于N*)
问若若A1A2+A2A3+……+AnA(n+1)>16/33,求n取值范围
人气:277 ℃ 时间:2019-10-23 06:21:33
解答
An+1=an/1+2an两边去倒数
1/an+1-1/an=2
1/an=1+(n+1)*2=2n+3
an=1/[2n+3]
a1a2+a2a3+……+anan+1=1/2[1/a1-1/a2+1/a2-a/a3+……-1/(2n+3)]=1/2-1/2(2n+3)>16/33
n>15
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