数列an满足,a(n+1)=1+1/(1+an),证明an的极限是根号2
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数列an满足,a(n+1)=1+1/(1+an),证明an的极限是根号2数列an满足,a(n+1)=1+1/(1+an),证明an的极限是根号2数列an满足,a(n+1)=1+1/(1+an),证明a
数列an满足,a(n+1)=1+1/(1+an),证明an的极限是根号2
数列an满足,a(n+1)=1+1/(1+an),证明an的极限是根号2
数列an满足,a(n+1)=1+1/(1+an),证明an的极限是根号2
当n→∞时
设lima(n+1)=liman=k
则k=1+1/(1+k)
k(1+k)=1+k+1
k²=2
解得k=√2
即liman=√2
a(n+1) = 1 + 1/(1+an)
两边同减√2
a(n+1) - √2 = (an-√2) / [(1+√2)(1+an)]
所以关键在于证明an有界且终将大于0,且存在N当n>N时0 < an < M
这么晚了,不继续写了:-)
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