(1)若项数为偶数项2n则 s偶-s奇=nd s偶/s奇=An/An-1(n大于等于2)(2)若项数为奇数项2n+1则s奇-s偶=An+1 s奇=(n+1)An+1 s偶=nAn+1 s偶/s奇=n/n+1 怎么推导出来的?数列知识
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![(1)若项数为偶数项2n则 s偶-s奇=nd s偶/s奇=An/An-1(n大于等于2)(2)若项数为奇数项2n+1则s奇-s偶=An+1 s奇=(n+1)An+1 s偶=nAn+1 s偶/s奇=n/n+1 怎么推导出来的?数列知识](/uploads/image/z/8377361-17-1.jpg?t=%EF%BC%881%EF%BC%89%E8%8B%A5%E9%A1%B9%E6%95%B0%E4%B8%BA%E5%81%B6%E6%95%B0%E9%A1%B92n%E5%88%99+s%E5%81%B6-s%E5%A5%87%3Dnd+s%E5%81%B6%2Fs%E5%A5%87%3DAn%2FAn-1%EF%BC%88n%E5%A4%A7%E4%BA%8E%E7%AD%89%E4%BA%8E2%EF%BC%89%EF%BC%882%EF%BC%89%E8%8B%A5%E9%A1%B9%E6%95%B0%E4%B8%BA%E5%A5%87%E6%95%B0%E9%A1%B92n%2B1%E5%88%99s%E5%A5%87-s%E5%81%B6%3DAn%2B1+s%E5%A5%87%3D%EF%BC%88n%2B1%EF%BC%89An%2B1+s%E5%81%B6%3DnAn%2B1+s%E5%81%B6%2Fs%E5%A5%87%3Dn%2Fn%2B1+%E6%80%8E%E4%B9%88%E6%8E%A8%E5%AF%BC%E5%87%BA%E6%9D%A5%E7%9A%84%3F%E6%95%B0%E5%88%97%E7%9F%A5%E8%AF%86)
(1)若项数为偶数项2n则 s偶-s奇=nd s偶/s奇=An/An-1(n大于等于2)(2)若项数为奇数项2n+1则s奇-s偶=An+1 s奇=(n+1)An+1 s偶=nAn+1 s偶/s奇=n/n+1 怎么推导出来的?数列知识
(1)若项数为偶数项2n则 s偶-s奇=nd s偶/s奇=An/An-1(n大于等于2)
(2)若项数为奇数项2n+1则s奇-s偶=An+1 s奇=(n+1)An+1 s偶=nAn+1 s偶/s奇=n/n+1 怎么推导出来的?
数列知识
(1)若项数为偶数项2n则 s偶-s奇=nd s偶/s奇=An/An-1(n大于等于2)(2)若项数为奇数项2n+1则s奇-s偶=An+1 s奇=(n+1)An+1 s偶=nAn+1 s偶/s奇=n/n+1 怎么推导出来的?数列知识
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)