A New Method of Power Sum for Natural Numbers

QIAO Shenyuan; LIANG Yikong

Volume 34 Issue 4

Dec. 2020

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QIAO Shenyuan, LIANG Yikong. A New Method of Power Sum for Natural Numbers[J]. Journal of Shanghai University of Engineering Science, 2020, 34(4): 392-396.

Citation:

QIAO Shenyuan, LIANG Yikong. A New Method of Power Sum for Natural Numbers[J]. Journal of Shanghai University of Engineering Science, 2020, 34(4): 392-396.

QIAO Shenyuan, LIANG Yikong. A New Method of Power Sum for Natural Numbers[J]. Journal of Shanghai University of Engineering Science, 2020, 34(4): 392-396.

Citation:

QIAO Shenyuan, LIANG Yikong. A New Method of Power Sum for Natural Numbers[J]. Journal of Shanghai University of Engineering Science, 2020, 34(4): 392-396.

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A New Method of Power Sum for Natural Numbers

QIAO Shenyuan^a
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LIANG Yikong^{b
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a.
School of Urban Rail Transportation
b.
School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China

Received Date: 2020-05-05
Publish Date: 2020-12-30

Abstract

Abstract

A function integral and form extension of the power sum of natural numbers was studied. By using Taylor expansion and the extended mean value theorem of integrals, the series expansion of the integral form of any real number power was given. Some examples were given to verify the effectiveness of the expansion.
- power sum for natural numbers,
- Taylor expansion,
- series expansion,
- mean value theorem of integrals

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References(8)

References

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