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consecutive sums

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What kinds of numbers can be written as the sum of consecutive whole numbers? How many ways can you write a whole number as the sum of consecutive whole numbers? For instance 9 = 5+4 and 9 = 2+3+4. Is it possible to tell if a number can be written as the sum of a given number of consecutive whole numbers? For instance, can 101 be written as the sum of five consecutive whole numbers?

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Solution Summary

This solution helps explore consecutive sums within the context of basic algebra.

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Suppose a number (a positive integer) N is given, and we'd like to determine whether N can be written as a sum of two consecutive positive integers, say; call them x and x + 1. If this were possible, then the equation

N = x + (x + 1)

would be solvable for x. This equation is ...

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