Sums I: The Gauss Sum

Algebra Level 1

As a young boy, Gauss was able to calculate math quickly. He was asked for the value of

\[ 1 +2 + 3 + \cdots + 100. \]

What was Gauss' answer?

Hint: \(1 + 2 + 3 + \cdots + n = \frac 12 n(n+1) \).


Image Source: Wikipedia.
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