作业帮已知数列{an}满足a1=33,an+1-an=2n 则求an/n?
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已知数列{an}满足a1=33,an+1-an=2n 则求an/n?
已知数列{an}满足a1=33,an+1-an=2n 则求an/n?
已知数列{an}满足a1=33,an+1-an=2n 则求an/n?
a(n+1)-an=2n
an-a(n-1)=2(n-1)-----------(1)
a(n-1)-a(n-2)=2(n-2)-------(2)
……………………
a2-a1=2×1-------------- (n-1)
(1)+(2)+...+(n-1)得 an-a1=2×[1+...+(n-2)+(n-1)]=2×[1+(n-1)](n-1)/2=n(n-1)
∴an=a1+n(n-1)=n²-n+33
an/n=n-1-33/n=n+33/n-1
[n(n-1)+33]/n
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