The sums of powers of the first n positive integers =0, 1, 2, ... ) satisfy the fundamental identity from which we can successively compute S_0 (n), S_1 (n), S_2 (n), etc. Identity (1) can easily be proved by using the binomial theorem; see e.g. [1, 2]. Several variations of (1) are also well known [3,4, 5].
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