等差数列中S奇 和 S偶 还有S奇除以S偶 S偶除以S奇 S奇减S偶 S偶减S奇的公式
发布网友
发布时间：2022-05-05 20:05
共1个回答
热心网友
时间：2023-10-09 12:00
a(2n) = a + (2n-1)d = (a + d) + (2n-2)d = (a+d) + (n-1)(2d).
a(2n-1) = a + (2n-2)d = a + (n-1)(2d).
S偶 = a(2) + a(4) + ... + a(2n) = n(a+d) + n(n-1)d = na + n^2d = n(a + nd) = na(n+1)
项数为2n+1时，S奇 = a(1) + a(2) + ... + a(2n-1) + a(2n+1) = (n+1)a + n(n+1)d = (n+1)[a + nd] = (n+1)a(n+1).
S奇/S偶 = (n+1)a(n+1)/[na(n+1)] = (n+1)/n.
S偶/S奇 = n/(n+1).
S奇 - S偶 = (n+1)a(n+1) - na(n+1) = a(n+1) = a + nd.
S偶 - S奇 = -a(n+1) = -a - nd.
项数为2n时，S奇 = a(1) + a(2) + ... + a(2n-1) = na + (n-1)nd = n[a + (n-1)d] = na(n).
S奇/S偶 = na(n)/[na(n+1)] = a(n)/a(n+1) = [a+(n-1)d]/(a+nd).
S偶/S奇 = a(n+1)/a(n) = (a+nd)/[a+(n-1)d].
S奇 - S偶 = na(n) - na(n+1) = n[a(n) - a(n+1)] = -nd.
S偶 - S奇 = n[a(n+1) - a(n)] = nd.追问项数为2n+1时，没有S偶么 还有项数为2n的时候没有S偶么
还有一开始的S奇呢
还有
追答无论项数为2n+1,还是2n, S奇都等于a(2)+a(4)+...+a(2n) = na(n+1).
