已知数列an满足a1=100,a(n+1)-an=2n,则(an)/n的最小值为

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已知数列an满足a1=100,a(n+1)-an=2n,则(an)/n的最小值为
已知数列an满足a1=100,a(n+1)-an=2n,则(an)/n的最小值为

已知数列an满足a1=100,a(n+1)-an=2n,则(an)/n的最小值为
a(n+1)-an=2n
an-a(n-1)=2(n-1)
…
a2-a1=2*1
相加：an-a1=2*[1+...+(n-2)+(n-1)]=n(n-1)
an=a1+n(n-1)=n²-n+100
an/n=n+100/n-1≥2√100-1=19
n=33/n n=5,6
a5/5=10.6,a6/6=10.5＜10.6
∴最小值10.5

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