已知数列｛An｝满足A1=33,A(n+1)-An=2n,则An/n的最小值为多少?答案是21/2,

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已知数列｛An｝满足A1=33,A(n+1)-An=2n,则An/n的最小值为多少?答案是21/2,
已知数列｛An｝满足A1=33,A(n+1)-An=2n,则An/n的最小值为多少?答案是21/2,

已知数列｛An｝满足A1=33,A(n+1)-An=2n,则An/n的最小值为多少?答案是21/2,
累加法：因为A(n+1)-An=2n,
所以：An-A(n-1)=2(n-1)
A(n-1)-A(n-2)=2(n-2)
A(n-2)-A(n-3)=2(n-3)
.
.
.
A2-A1=2*1
累加,得：An-A1=2(1+2+3+.+n-1)=n(n-1)
因为A1=33,所以：An=n(n-1)+33
An/n=n-1+33/n=n+33/n-1
要求最小值,函数思想：
n+33/n是对勾函数（也称耐克函数）,勾底是√33,5

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