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Text File  |  1991-10-28  |  677b  |  23 lines
  1. sum(n) = n*(n+1)/2
  2. sum(n^2) = n*(n+1)*(2*n+1)/6
  3. sum(n^3) = n^2*(n+1)^2/4
  4. sum((-1)^(n-1)*n^2) = (-1)^(n-1)*n*(n+1)/2
  5. sum(2*n) = n*(n+1)
  6. sum(2*n-1) = n^2
  7. sum((2*n-1)^2) = n*(4*n^2-1)/3
  8. sum((2*n-1)^3) = n^2*(2*n^2-1)
  9.  
  10. sum(j!*j, j from 1 to n) = (n+1)!-1
  11. sum(j/(j+1)!, j from 1 to n) = 1-1/(n+1)!
  12. sum(1/(j!*(n-j)!), j from 0 to n) = 2^n/n!
  13.  
  14. sum(1/n!, n from 0 to inf) = e
  15. sum((-1)^n/n!, n from 0 to inf) = 1/e
  16. sum(x^n/n!, n from 0 to inf) = e^x
  17. sum((-1)^n*x^(2*n+1)/(2*n+1)!, n from 0 to inf) = sin(x)
  18. sum((-1)^n*x^(2*n)/(2*n)!, n from 0 to inf) = cos(x)
  19. sum(x^(2*n+1)/(2*n+1)!, n from 0 to inf) = sinh(x)
  20. sum(x^(2*n)/(2*n)!, n from 0 to inf) = cosh(x)
  21.  
  22. end
  23.