应该有一个等差数列的条件,
(1)S偶-S奇
=[a2+a4+a6+.+a(2n)]-[a1+a3+a5+.+a(2n-1)]
=(a2-a1)+(a4-a3)+(a6-a5)+.+[a(2n)-a(2n-1)]
= d+d+d+.+d (n个d)
=nd
S偶=a2+a4+a6+.+a(2n)=[a(2)+a(2n)]*n/2=2a(n+1)*n/2=na(n+1)
S奇=a1+a3+a5+.+a(2n-1)=[a(1)+a(2n-1)]*n/2=2a(n)*n/2=na(n)
∴ S偶/S奇=a(n+1)/a(n)
你给的结果不对.
(2)
S奇-S偶
=[a1+a3+a5+.+a(2n-1)+a(2n+1)]-[a2+a4+a6+.+a(2n)]
=a1+(a3-a2)+(a5-a4)+(a7-a6)+.+[a(2n+1)-a(2n)]
= a1+d+d+d+.+d (n个d)
=a1+nd
=a(n+1)
S偶=a2+a4+a6+.+a(2n)=[a(2)+a(2n)]*n/2=2a(n+1)*n/2=na(n+1)
S奇=a1+a3+a5+.+a(2n-1)+a(2n+1)=[a(1)+a(2n+1)]*(n+1)/2=2a(n+1)*(n+1)/2=(n+1)a(n+1)
∴ S偶/S奇=n/(n+1)