等差数列{An}中,A1大于0,S12大于0,S13小于0,求S1,S2 ...S12哪一个最大
问题描述:
等差数列{An}中,A1大于0,S12大于0,S13小于0,求S1,S2 ...S12哪一个最大
答
设等差数列的公差为d,首项为A1
由等差数列前n项和S=nA1+n*(n-1)*d/2得:
S12=12*A1+12*(12-1)*d/2=12A1+66d=12(A1+5.5d)
S13=13A1+13(13-1)*d/2=13A1+78d=7(A1+6d)
而:S12>0,S130 ,A1+5.5d>0
7(A1+6d)