Maths MC
2007-11-18 6:07 am
Please complete the following MC with explanations.
Under which of the following conditions must the mean of n consecutive positive integers also be an integer?
A.
n is any positive integer
B.
n is any positive odd integer
C.
n is any positive even integer
D.
n is any multiple of 3
E.
n is the square of any positive integer
回答 (1)
2007-11-18 6:24 am
✔ 最佳答案
The answer is B.Consider the n consecutive integers are a, a+1, a+2, ..., a+ (n-1), where is a an integer.
Mean of n integers = (a+a+1+a+2+...+a+n-1)/n
= (na + 1 + 2 + ... + (n-1))/n
= [na + (n-1)n/2] / n
= [a + (n-1)/2]
Hence only when n is an odd integer, (n-1)/2 could be an integer, i.e. a + (n-1)/2 is also an integer.
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