一個(gè)有2n+1項(xiàng)的等差數(shù)列,其奇數(shù)項(xiàng)之和與偶數(shù)項(xiàng)之和的比為----

數(shù)學(xué)人氣：865 ℃時(shí)間：2019-09-18 05:29:43

優(yōu)質(zhì)解答

設(shè)原數(shù)列首項(xiàng)為a,公差為d,
原數(shù)列依次為a,a+d,a+2d,a+3d,.,a+2nd
奇數(shù)項(xiàng)為：a,a+2d,a+4d,.,a+2nd
奇數(shù)項(xiàng)和：S奇 = [a + (a+2nd)](n+1)/2 = (a+nd)(n+1)
偶數(shù)項(xiàng)為：a+d,a+3d,a+5d,.,a+(2n-1)d
偶數(shù)項(xiàng)和：S偶 = [(a+d) + (a+2nd-d)]n/2 = (a+nd)n
S奇/S偶 = (n+1)/n
說明：
本題只需用到等差數(shù)列求和公式：(首項(xiàng)+尾項(xiàng))×項(xiàng)數(shù)÷2