SOLUTION: The sum of 99 consecutive odd, positive integers is the greatest perfect cube less than 999 999. Find the sum of the least and the greatest of the integers.

Question 1147619: The sum of 99 consecutive odd, positive integers is the greatest perfect cube less than 999 999. Find the sum of the least and the greatest of the integers.
Answer by ikleyn(52855) (Show Source): You can put this solution on YOUR website!
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(1)  Notice that the sum of 99 consecutive odd integers is 99 times the average of the first and the last numbers in this sequence.



(2)  In other words,  the sum of 99 consecutive odd integers is 99 times half the sum of the first and the last numbers in this sequence.



(3)   = 99.99997... (approximately)

     It means that the greatest perfect cube less than 999999 is .



(4)  Thus the condition says

          = .



(5)  Hence,   +  =  = 19602.


     It is the ANSWER to the problem's question.

Solved.

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