求高手帮我解题,是数列中的已知递推求通项的题数列｛an｝中an＝1.an+1＝an+2n-1.求an＝?

Question

求高手帮我解题,是数列中的已知递推求通项的题
数列｛an｝中an＝1.an+1＝an+2n-1.求an＝?

Answer 1

递推法：
an+1＝an+2n-1
an＝a(n-1)+2(n-1)-1
an-1＝a(n-2)+2(n-2)-1
...
a2=a1+2-1;
叠加an+1=2(n+n-1+n-2...+2+1)-n+a1=n(n+1)-n+1=n^2+1,
an=(n-1)^2+1;