Faulhaber's Formula
In a 1631 edition of Academiae Algebrae, J. Faulhaber published the general formula for the Sum of 
th Powers of the first 
Positive Integers,
 | (1) |
is the Kronecker Delta, 
is a Binomial Coefficient,and 
is the 
th Bernoulli Number. Computing the sums for 
, ..., 10 gives |  |  | (2) |
 | |  | (3) |
 | |  | (4) |
 | |  | (5) |
 | |  | (6) |
 | |  | (7) |
 | |  | (8) |
 | |  | (9) |
 | |  | (10) |
 | |  | (11) |
See also Power, Sum
References
Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, p. 106, 1996.
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