Otecald: Sumatoria de potencias

Sumatoria de potencias

s(x,1) = x^2/2 + x/2

s(x,2) = x^3/3 + x^2/2 + x/6

s(x,3) = x^4/4 + x^3/2 + x^2/4

s(x,4) = x^5/5 + x^4/2 + x^3/3 - x/30

s(x,5) = x^6/6 + x^5/2 + 5x^4/12 - x^2/12

s(x,6) = x^7/7 + x^6/2 + x^5/2 - x^3/6 + x/42

s(x,7) = x^8/8 + x^7/2 + 7x^6/12 - 7x^4/12 + x^2/12

s(x,8) = x^9/9 + x^8/2 + 2x^7/3 - 7x^5/15 + 2x^3/9

s(x,9) = x^10/10 + x^9/2 + 3x^8/4 - 7x^6/10 + x^4/2 + x^2/10

s(x,10) = x^11/11 + x^10/2 + x^9 - 5x^8/3 - x^7 + x^5 - 5x^3/9

Las imágenes siguientes fueron generadas por un sitio web.

s(x,1) = x^2/2+x/2

$s\left ( x,1 \right )=\frac{x^{2}}{2}+\frac{x}{2}$

s(x,2) = x^3/3+x^2/2+x/6

$s\left ( x,2 \right )= \frac{x^3} {3} +\frac{x^2}{2} +\frac{x} {6}$

s(x,3) = x^4/4+x^3/2+x^2/4

$s\left ( x,3 \right )= \frac{x^4}{4} +\frac{x^3}{2} +\frac{x^2}{4}$

s(x,4) = x^5/5+x^4/2+x^3/3-x/30

$s\left ( x,4 \right )= \frac{x^5}{5 } +\frac{x^4}{2 } +\frac{x^3}{3 } -\frac{x }{30}$

s(x,5) = x^6/6+x^5/2+5x^4/12-x^2/12

$s\left ( x,5 \right )= \frac{x^6 }{6 } +\frac{x^5 }{2 } +\frac{5x^4}{12} -\frac{x^2 }{12}$

s(x,6) = x^7/7+x^6/2+x^5/2-x^3/6+x/42

$s\left ( x,6 \right )= \frac{x^7 }{7 } +\frac{x^6 }{2 } +\frac{x^5 }{2} -\frac{x^3 }{6} +\frac{x }{42}$

s(x,7) = x^8/8+x^7/2+7x^6/12-7x^4/12+x^2/12

$s\left ( x,7 \right )= \frac{x^8 }{8 } +\frac{x^7 }{2 } +\frac{7x^6}{12} -\frac{7x^4}{12} +\frac{x^2 }{12}$

s(x,8) = x^9/9+x^8/2+2x^7/3-7x^5/15+2x^3/9

$s\left ( x,8 \right )= \frac{x^9 }{9 } +\frac{x^8 }{2 } +\frac{2x^7}{3 } -\frac{7x^5}{15} +\frac{2x^3}{9 }$

s(x,9) = x^10/10+x^9/2+3x^8/4-7x^6/10+x^4/2+x^2/10

$s\left ( x,9 \right )= \frac{x^{10}}{10} +\frac{x^9 }{2 } +\frac{3x^8}{4 } -\frac{7x^6}{10} +\frac{x^4 }{2 } +\frac{x^2 }{10}$

s(x,10) = x^11/11+x^10/2+x^9-5x^8/3-x^7+x^5-5x^3/9

$s\left ( x,10 \right )= \frac{x^{11}}{11} +\frac{x^{10}}{2 } +x^9 -\frac{5x^8 }{3 } -x^7 +x^5 -\frac{5x^3 }{9}$

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