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02-genfunc.tex

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May 7th, 2025
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Latex 0.65 KB | Source Code | 0 0
  1. \documentclass{article}
  2.  
  3. \usepackage{amsmath}
  4. \usepackage{newpxtext}
  5. \usepackage{eulervm}
  6.  
  7. \pagestyle{empty}
  8.  
  9. \begin{document}
  10.  
  11. \[
  12. \everymath={\displaystyle}
  13. \begin{array}{l@{\ }l@{\ }l}
  14. \sum_{n = 0}^\infty F_n x^n
  15. & = & 0x^0 + 1x^1 + \sum_{n = 2}^\infty (F_{n - 1} + F_{n - 2}) x^n \\
  16. & = & 0x^0 + 1x^1 + \sum_{n = 2}^\infty F_{n - 1} x^n + \sum_{n = 2}^\infty F_{n - 2} x^n \\
  17. & = & 0x^0 + 1x^1 + \sum_{n = 0}^\infty F_n x^{n + 1} + \sum_{n = 0}^\infty F_n x^{n + 2} \\
  18. \\
  19. \rlap{$\left( \sum_{n = 0}^\infty F_n x^n \right) (1 - x - x^2) = x$} \\
  20. \sum_{n = 0}^\infty F_n x^n
  21. & = & \frac{-x}{x^2 + x - 1}
  22. \end{array}
  23. \]
  24.  
  25. \end{document}
  26.  
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