23等差数列{an}
证明:
等差数列{an},有an = a0 + (n - 1)*d
Sn = n*a0 + n*(n - 1)*d/2
(1)S12 = 12a0 + 66d
当2*a0 + 11d>0时,有S12>0,比如,a0 = 1,d =1,显然S12>0,但公差d的取值范围不在(-24/7,-3)
因此
S12>0=/=>公差的取值范围是(-24/7,-3)
(2)S13 = 13a0 + 78d
当a0 + 6d公差的取值范围是(-24/7,-3)
(3)
S12 = 12a0 + 66d >0
S13 = 13a0 + 78d d > -2a0/11
-2a0/11 >-3 => a0 a...全部
证明:
等差数列{an},有an = a0 + (n - 1)*d
Sn = n*a0 + n*(n - 1)*d/2
(1)S12 = 12a0 + 66d
当2*a0 + 11d>0时,有S12>0,比如,a0 = 1,d =1,显然S12>0,但公差d的取值范围不在(-24/7,-3)
因此
S12>0=/=>公差的取值范围是(-24/7,-3)
(2)S13 = 13a0 + 78d
当a0 + 6d公差的取值范围是(-24/7,-3)
(3)
S12 = 12a0 + 66d >0
S13 = 13a0 + 78d d > -2a0/11
-2a0/11 >-3 => a0 a0 > 144/7
当a0 144/7时,公差d的取值范围不在(-24/7,-3)。
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