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Sums of Powers of the Integers

Published online by Cambridge University Press:  03 November 2016

R. V. Parker
R. V. Parker*
Affiliation:
Bressingham, Diss, Norfolk
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Extract

Recent Notes in the Mathematical Gazette have suggested directly or by implication the surprise felt by some students of mathematics when Σx3 turns out to be (Σx)2, Perhaps the results appear less surprising if they are seen, not in isolation, but as two particular cases of summation formulae for odd powers of the integers expressed in powers of {x(x + 1)}.

The fact that the sums of odd powers of the integers are expressible in powers of {x(x + 1)} can be used as a demonstration of the distinctive pattern of the difference tables of these sums, which facilitates their speedy calculation.

Type
Research Article
Information
The Mathematical Gazette , Volume 42 , Issue 340 , May 1958 , pp. 91 - 95
Copyright
Copyright © Mathematical Association 1958

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References

1. Nicholson, A. N., “Identities in Sums of Powers of Integers”;Wheeler, Roger F., “On Σr 3 = (Σr)2 ”; Mathematical Gazette, May, 1957, pp. 114 and 122. et al.Google Scholar
2. Piza, Pedro A., “Powers of Sums and Sums of Powers,” Mathematics Magazine, January-February, 1952, pp. 137–42.Google Scholar
3. Milne-Thomson, L. M., The Calculus of Finite Differences, Macmillan, 1951, pp. 22 and 63.Google Scholar
4. Milne-Thomson, L. M., op. cit., p. 65.Google Scholar