Closed Form for Triangular Numbers/Direct Proof/Historical Note
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Historical Note on Closed Form for Triangular Numbers: Direct Proof
This direct proof is the method supposedly employed by Carl Friedrich Gauss who, when very young (according to the apocryphal story), calculated the sum of the numbers from $1$ to $100$ before the teacher had barely sat back down after setting the assignment.
Whether this story is actually true or not is the subject of speculation.
Sources
- 2000: Michael R.A. Huth and Mark D. Ryan: Logic in Computer Science: Modelling and reasoning about systems ... (previous) ... (next): $\S 1.4.2$: Mathematical induction