Abstract

But we know that one who does this by merely adding terms one after another is not seeing the forest for the trees. An anecdote about young Gauss tells us that he solved the above problem by noticing that pairwise addition of terms from opposite ends of the list yields identical intermediate sums. This famous story is well told by Hayes in [5], with references. A very convenient way to express Gauss’s idea is to write down the series twice, once in ascending and once in descending order,

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