mathematical thinking

If you have a slight teeny-weeny interest in mathematics then you must have heard of Gauss’childhood story.
As an elementary student he amazed his teacher by quickly finding the sum of the integers from 1 to 100. Gauss recognized he had fifty pairs of numbers when he added the first and last number in the series, the second and second-last number in the series, and so on. For example: (1 + 100), (2 + 99), (3 + 98), . . . , and each pair has a sum of 101.

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