Question

数列 an=2n-2,n为奇数,an=2n+1,n为偶数,求前n项和sn

Answer 1

if n 奇数

Sn = (n+1)(an+a1)/4 + (n-1)((a2+a(n-1))/4

= (n+1)(2n-2)/4 +(n-1)( 5 + 2(n-1)+1)/4

= (n+1)(2n-2)/4 + (n-1)(2n-4)/4

=(1/2)(n-1)(n+1+n-2)

= (1/2)(n-1)(2n-1)

if n 偶数

Sn= n(a(n-1)+a1)/4 + n(a2+an)/4

= n(2(n-1)-2)/4 + n(5+2n+1)/4

= n(n-2)/2 + n(n+3)/2

= (1/2)n(n-2+n+3)

=(1/2)n(2n-1)