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標題:

maths

發問:

1. how many three digit numbers are divisible by12 ? (tips : use series and squence to calculate ) 2. find the sum of all the positive terms in the geometric sequence 27,-9, 3, -1............ ans : 30.075 thx 更新: 六呎將軍-b- 第2條問既系sum of +ve terms...

最佳解答:

(1) The smallest 3-digit value divisible by 12 is 108. So setting up an arithmetic sequence with first term = 108 and common difference = 12, we have: 108 + 12(n - 1) < 1000 where n is the no. of 3-digit values divisible by 12. 12(n - 1) < 892 n - 1 < 223/3 n < 226/3 n = 75 So 75 3-digit numbers are divisible by 12. (2) First term = 27, common difference = -1/3 Thus, when summing up to infinite no. of terms: S = a/(1 - R) = 27/(1 + 1/3) = 20.25 2009-03-18 11:29:46 補充： First term = 27, common difference = 1/9 Thus, when summing up to infinite no. of terms: S = a/(1 - R) = 27/(1 - 1/9) = 30.375

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