数列an满足a1=1,an=an-1+1/n方-n(n大于等于2),求an通项

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数列an满足a1=1,an=an-1+1/n方-n(n大于等于2),求an通项

数列an满足a1=1,an=an-1+1/n方-n(n大于等于2),求an通项
数列an满足a1=1,an=an-1+1/n方-n(n大于等于2),求an通项

数列an满足a1=1,an=an-1+1/n方-n(n大于等于2),求an通项
an=a(n-1)+1/(n²-n)=a(n-1)+1/(n-1)-1/n
an+1/n=a(n-1)+1/(n-1)
an+1/n=a(n-1)+1/(n-1)=a(n-2)+1/(n-2)=...=a1+1/1=1+1=2
an=2-1/n=(2n-1)/n
n=1时,a1=(2-1)/1=1,同样满足.
数列{an}的通项公式为an=(2n-1)/n