若数列{an}满足a1=√(6),an+1=√(an+6),(n∈N),如果lim(an)存在,求lim(an)n都趋向无穷大
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若数列{an}满足a1=√(6),an+1=√(an+6),(n∈N),如果lim(an)存在,求lim(an)n都趋向无穷大
若数列{an}满足a1=√(6),an+1=√(an+6),(n∈N),如果lim(an)存在,求lim(an)
n都趋向无穷大
若数列{an}满足a1=√(6),an+1=√(an+6),(n∈N),如果lim(an)存在,求lim(an)n都趋向无穷大
设lima(n)=A
a(n+1)=根号(a(n)+6)
两边平方,得
(a(n+1))^2=a(n)+6
令n趋向无穷大,两边求极限,得
A^2=A+6
解得A=3或-2
由题设易证a(n)恒≥0,故A≥0
所以lima(n)=A=3
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