We know that Gauss has shown that the sum S of the first n natural numbers is given by the relation:
S=n(n+1)2
The proof that I remember most frequently is as follows:
Let be S=1+2+⋯+(n−1)+n We can write S it also as: S=n+(n−1)+⋯+2+1.
By adding up member to member we get:
2S=(n+1)+(n+1)+⋯+2+1⏟n−times.
Hence we obtain the (∗).
How many other simple methods exist to calculate the sum of the first natural numbers?
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