The third power of positive integer m greater than 1 can be "split" into the sum of several consecutive odd numbers, such as 23=3+5, 33=7+9

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The third power of positive integer m greater than 1 can be "split" into the sum of several consecutive odd numbers, such as 23=3+5, 33=7+9+11, 43=13+15+17+19,... If m3 is split, one of the odd numbers is 2013, then the value of m is [] A.43B.44 C.45D.46

Best answer:

C。

Answer analysis:

Classification and induction (change of numbers).

[Analysis] Analyze the rule, and then find out the range of odd numbers where 2013 is, to get the solution:

∵23＝3＋5，33＝7＋9＋11，43＝13＋15＋17＋19。

…

 m3 The first number after splitting is m (m-1)+1, and there are m odd numbers in total.

∵45×(45－1)＋1＝1981，46×(46－1)＋1＝2071。

 The 2013 odd number is an odd number after the cube of the number with base 45 is split.

∴m＝45。 So select C.

Test core:

Definition of rational number: rational number is the general name of integer and fraction. All rational numbers can be transformed into fractions.

Lonely Traveler 2024-06-21 13:43:42

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