已知数列{an}满足a1=33,a(n+1)-an=2n,则an/n的最小值

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已知数列{an}满足a1=33,a(n+1)-an=2n,则an/n的最小值已知数列{an}满足a1=33,a(n+1)-an=2n,则an/n的最小值已知数列{an}满足a1=33,a(n+1)-a

已知数列{an}满足a1=33,a(n+1)-an=2n,则an/n的最小值
已知数列{an}满足a1=33,a(n+1)-an=2n,则an/n的最小值

已知数列{an}满足a1=33,a(n+1)-an=2n,则an/n的最小值
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+33
an/n=n+33/n-1≥2√33-1
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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