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The sum of n different positive integers is less than 100. What is the greatest possible value of n?
The sum of n different positive integers is less than 100. What is the greatest possible value of n?
admin
2009-05-19
42
问题
The sum of n different positive integers is less than 100. What is the greatest possible value of n?
选项
A、10
B、11
C、12
D、13
E、14
答案
D
解析
n个不同正整数的和小于100,问n的最大值(the greatest possible value)是多少?
解:本题的正确答案是(D)。要求n的最大值,就要使每个加数都尽可能的小。而题中已限制加数为不同的正整数,所以要使加数的个数最多,只能从最小正整数开始,依次从小到大取值,即1+2+3……<100。任取n=13,则1加至13的和为91,小于100而不可能再加上14,否则将不能满足小于100的条件。
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