若数列an满足a1=√6,a(n+1)=√(an+6),如果lim(an)存在,求lim(an)n趋向于无穷,n属于N*,√是根号的意思谢谢
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![若数列an满足a1=√6,a(n+1)=√(an+6),如果lim(an)存在,求lim(an)n趋向于无穷,n属于N*,√是根号的意思谢谢](/uploads/image/z/7141627-19-7.jpg?t=%E8%8B%A5%E6%95%B0%E5%88%97an%E6%BB%A1%E8%B6%B3a1%3D%E2%88%9A6%2Ca%28n%2B1%29%3D%E2%88%9A%28an%2B6%29%2C%E5%A6%82%E6%9E%9Clim%EF%BC%88an%EF%BC%89%E5%AD%98%E5%9C%A8%2C%E6%B1%82lim%EF%BC%88an%EF%BC%89n%E8%B6%8B%E5%90%91%E4%BA%8E%E6%97%A0%E7%A9%B7%2Cn%E5%B1%9E%E4%BA%8EN%2A%2C%E2%88%9A%E6%98%AF%E6%A0%B9%E5%8F%B7%E7%9A%84%E6%84%8F%E6%80%9D%E8%B0%A2%E8%B0%A2)
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若数列an满足a1=√6,a(n+1)=√(an+6),如果lim(an)存在,求lim(an)n趋向于无穷,n属于N*,√是根号的意思谢谢
若数列an满足a1=√6,a(n+1)=√(an+6),如果lim(an)存在,求lim(an)
n趋向于无穷,n属于N*,√是根号的意思
谢谢
若数列an满足a1=√6,a(n+1)=√(an+6),如果lim(an)存在,求lim(an)n趋向于无穷,n属于N*,√是根号的意思谢谢
如果极限存在的话,对a(n+1)=√(an+6)两边求极限,设lim(an)=a,则:
lim a(n+1)=a=lim √(an+6)=√(a+6)
即:a^2=a+6,a=3 或-2(舍去).
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