Prove that the sum of first n natural numbers is $$n(n+1)\over 2$$

Solution :

Let $$S_n$$ = 1 + 2 + 3 + ….. + n = $$\sum_{k=1}^{n} k$$

Clearly, it is an arithmetic series with first term a = 1, common difference d = 1 and last term l = n.

$$\therefore$$ $$S_n$$ = $$n\over 2$$ (1 + n) = $$n(n+1)\over 2$$

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