Question

求高手帮我解题,是数列中的已知递推求通项的题

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;