oo ____ \ ` \ n 2*n + 1 \ (-1) *x / -------------- / (2*n + 1)! /___, n = 10
Sum(((-1)^n*x^(2*n + 1))/factorial(2*n + 1), (n, 10, oo))
/ 4 8 12 16 18 14 10 6 2 \ 21 |-51090942171709440000 - 425757851430912000*x - 140792940288000*x - 8204716800*x - 143640*x + 420*x + 39070080*x + 1279935820800*x + 10137091700736000*x + 8515157028618240000*x 51090942171709440000*sin(x)| x *|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------| | 20 21 | \ x x / --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 51090942171709440000
x^21*((-51090942171709440000 - 425757851430912000*x^4 - 140792940288000*x^8 - 8204716800*x^12 - 143640*x^16 + 420*x^18 + 39070080*x^14 + 1279935820800*x^10 + 10137091700736000*x^6 + 8515157028618240000*x^2)/x^20 + 51090942171709440000*sin(x)/x^21)/51090942171709440000
x^n/n
(x-1)^n
1/2^(n!)
n^2/n!
x^n/n!
k!/(n!*(n+k)!)
csc(n)^2/n^3
1/n^2
1/n^4
1/n^6
1/n
(-1)^n
(-1)^(n + 1)/n
(n + 2)*(-1)^(n - 1)
(3*n - 1)/(-5)^n
(-1)^(n - 1)*n/(6*n - 5)
(-1)^(n + 1)/n*x^n
(3*n - 1)/(-5)^n