用数学归纳法
a1=2显然大于根号3
若a(k-1)>(2k-1)^0.5
ak=a(k-1)+1/a(k-1)>(2k-1)^0.5+1/(2k-1)^0.5=2n/(2k-1)^0.5>(2k+1)^0.5
故对于n属于正整数,an>(2n+1)^0.5
完了
设数列{an}满足a1=2,an+1=an+1/an,(n∈N).
3个回答
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