SOLUTION: What is the greatest number of consecutive positive integers whose sum is 585?

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Question 485869: What is the greatest number of consecutive positive integers whose sum is 585?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
We can say that

where a and n are integers. This simplifies to







If n = 585, then (n-1)/2 = 292 and we can set a = -291. We can check that (-291) + (-290) + ... + 291 + 292 + 293 = 585, because all the terms except 292 and 293 cancel (and 292 + 293 is obviously 585). Hence n = 585 is the greatest such number.