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Writing 100 as a sum of consecutive numbers

numberssumsdivisorsarithmetic-series

For example, 15 = 7 + 8 = 4 + 5 + 6 = 1 + 2 + 3 + 4 + 5, so 15 can be written as a sum of consecutive positive whole numbers in three ways (using at least two terms).

In how many ways can 100 be written as a sum of two or more consecutive positive whole numbers? List them.

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A run of k consecutive numbers starting at a adds up to k times a plus k(k minus 1)/2. Try each k in turn and see whether a comes out as a positive whole number.

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