Question

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

Answer 1

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