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~~Algebra~~

Logarithm Theorem Pythagorean Theorem Combinatorics Quadratic Equations Sequence and Series Linear Algebra Diophantine Equation Elliptic Curve~~Algebra Result~~

`-=[]⟨⟩\;',./~!@#$%^&*()_+{}|:"<>? 𝑎𝑏𝑐𝑑𝑒𝑓𝑔ℎ𝑖𝑗𝑘𝑙𝑚𝑛𝑜𝑝𝑞𝑟𝑠𝑡𝑢𝑣𝑤𝑥𝑦𝑧 Å − × ⋅∓±∘꞊﹦∗∙ ℯ 𝔸𝔹ℂ𝔻𝔼𝔽𝔾ℍ𝕀𝕁𝕂𝕃𝕄ℕ𝕆ℙℚℝ𝕊𝕋𝕌𝕍𝕎𝕏𝕐ℤ𝐴𝐵𝐶𝐷𝐸𝐹𝐺𝐻𝐼𝐽𝐾𝐿𝑀𝑁𝑂𝑃𝑄𝑅𝑆𝑇𝑈𝑉𝑊𝑋𝑌𝑍 ∼∽∾≁≂≃≄≅≆≇≈≉≌≐≠≡ ≤≥≦≧≨≩≪≫ ∈∉∊∋∌∍ ⊂⊃⊄⊅⊆⊇ 𝛼𝛽𝛾𝛿𝜀𝜁𝜂𝜃𝜄𝜅𝜆𝜇𝜈𝜉𝜊𝜋𝜌𝜎𝜏𝜐𝜑𝜒𝜓𝜔 ∀∂∃∅⦰∆∇∎∞∝∴∵ ∏∐∑⋀⋁⋂⋃ ∧∨∩∪ ∫∬∭∮∯∰∱∲∳ ∥⋮⋯⋰⋱ ‖ ′ ″ ‴ ⁄ ⁗ ʹ ʺ ‵ ‶ ‷ ﹁﹂﹃﹄︹︺︻︼ ︗ ︘ ︿﹀︽︾﹇﹈︷︸ ⏜ ⏝ ⎴ ⎵ ⏞ ⏟ ⏠ ⏡ ←↑→↓↤↦↥↧↔↕↖↗↘↙▲▼◀▶↺↻⟲⟳ ↼↽↾↿⇀⇁⇂⇃⇄⇅⇆⇇ ⇐⇑⇒⇓⇔⇌⇍⇏⇕⇖⇗⇘⇙⇙⇳⥢⥣⥤⥥⥦⥧⥨⥩⥪⥫⥬⥭⥮⥯

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Algebra
 Figurate Numbers
 Sources and References

Algebra

Figurate Numbers

The 𝑛^th term of any order is the sum of 𝑛 terms of the preceding order. The 𝑛^th term of the 𝑟^th order is 𝑛(𝑛+1)⋯(𝑛+𝑟−2)(𝑟−1)!=𝐻(𝑛,𝑟−1) By (98) 289 The sum of 𝑛 terms is 𝑛(𝑛+1)⋯(𝑛+𝑟−1)𝑟!=𝐻(𝑛,𝑟)

OrderFigurate Numbers𝑛^th term

            11,1,1,1,1,1,1
            2123456𝑛
            3136101521𝑛(𝑛+1)1⋅2
            41410203556𝑛(𝑛+1)(𝑛+2)1⋅2⋅3
            515153570126𝑛(𝑛+1)(𝑛+2)(𝑛+3)1⋅2⋅3⋅4
            6162156126252𝑛(𝑛+1)(𝑛+2)(𝑛+3)(𝑛+4)1⋅2⋅3⋅4⋅5

290

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:

References

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

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