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Algebra
 Figurate Numbers
 Sources and References

Algebra

Figurate Numbers

The 𝑛th term of any order is the sum of 𝑛 terms of the preceding order. The 𝑛th term of the π‘Ÿth order is 𝑛(𝑛+1)β‹―(𝑛+π‘Ÿβˆ’2)(π‘Ÿβˆ’1)!=𝐻(𝑛,π‘Ÿβˆ’1) By (98) 289 The sum of 𝑛 terms is 𝑛(𝑛+1)β‹―(𝑛+π‘Ÿβˆ’1)π‘Ÿ!=𝐻(𝑛,π‘Ÿ) OrderFigurate Numbers𝑛th term
11,1,1,1,1,1,1 2123456𝑛 3136101521𝑛(𝑛+1)1β‹…2 41410203556𝑛(𝑛+1)(𝑛+2)1β‹…2β‹…3 515153570126𝑛(𝑛+1)(𝑛+2)(𝑛+3)1β‹…2β‹…3β‹…4 6162156126252𝑛(𝑛+1)(𝑛+2)(𝑛+3)(𝑛+4)1β‹…2β‹…3β‹…4β‹…5
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Sources and References

https://archive.org/details/synopsis-of-elementary-results-in-pure-and-applied-mathematics-pdfdrive

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ID: 210600026 Last Updated: 6/26/2021 Revision: 0 Ref:

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References

  1. B. Joseph, 1978, University Mathematics: A Textbook for Students of Science & Engineering
  2. Wheatstone, C., 1854, On the Formation of Powers from Arithmetical Progressions
  3. Stroud, K.A., 2001, Engineering Mathematics
  4. Coolidge, J.L., 1949, The Story of The Binomial Theorem
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