Current location - Training Enrollment Network - Mathematics courses - Mathematical reasoning and proof questions, how to solve them, be more detailed.
Mathematical reasoning and proof questions, how to solve them, be more detailed.
According to the meaning in the question, 5 4 should be decomposed into several consecutive odd sums, assuming that it is n consecutive odd sums (n >;; 1)

1. Multiplied by two odd numbers, it is still an odd number. If 5 4 is odd, it is judged that n is odd, otherwise the sum is even.

2. Because it is a continuous odd number, that is, arithmetic progression, according to arithmetic progression's summation formula, when n is an odd number, the sum of the series must be an integer multiple of n ... so the minimum qualified n is 5, because obviously 5 4 is not a multiple of 3.

Assuming that n is 5, according to the characteristics of arithmetic progression, the average value (that is, the third odd number in the middle) = (5 4)/5 = 625/5 =125.

5^4 = 12 1 + 123 + 125 + 127 + 129