oo ____ \ ` \ n \ n*x n / -------*3 / 8*n - 9 /___, n = 2
Sum(((n*x^n)/(8*n - 9))*3^n, (n, 2, oo))
/ / / pi*I\ -3*pi*I / 5*pi*I\ -pi*I / 7*pi*I\ pi*I / pi*I\ 3*pi*I / 3*pi*I\ / 3*pi*I\\ | | | ----| ------- | ------| ------ | ------| ---- | ----| ------ | ------| | ------|| | | 8 ___ / 8 ___ 8 ___\ 8 ___ / 8 ___ 8 ___ pi*I\ 8 ___ | 8 ___ 8 ___ 2 | 8 ___ 4 | 8 ___ 8 ___ 4 | 8 ___ 4 | 8 ___ 8 ___ 4 | 8 ___ 4 | 8 ___ 8 ___ 4 | 8 ___ 4 | 8 ___ 8 ___ 4 | 8 ___ | 8 ___ 8 ___ 2 || | 2 | 7 21*\/ 3 *log\1 - \/ 3 *\/ x / 21*\/ 3 *log\1 - \/ 3 *\/ x *e / 21*I*\/ 3 *log\1 - \/ 3 *\/ x *e / 21*\/ 3 *e *log\1 - \/ 3 *\/ x *e / 21*\/ 3 *e *log\1 - \/ 3 *\/ x *e / 21*\/ 3 *e *log\1 - \/ 3 *\/ x *e / 21*\/ 3 *e *log\1 - \/ 3 *\/ x *e / 21*I*\/ 3 *log\1 - \/ 3 *\/ x *e /| |18*x *|- ---------- - ----------------------------- + ----------------------------------- - ------------------------------------- - ---------------------------------------------- - --------------------------------------------- - ----------------------------------------- - --------------------------------------------- + ---------------------------------------| | | -16 + 48*x 7/8 7/8 7/8 7/8 7/8 7/8 7/8 7/8 | | \ 128*x 128*x 128*x 128*x 128*x 128*x 128*x 128*x / |------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- for 3*|x| < 1 | 7 < | oo | ____ | \ ` | \ n n | \ n*3 *x | / -------- otherwise | / -9 + 8*n | /___, \ n = 2
Piecewise((18*x^2*(-7/(-16 + 48*x) - 21*3^(1/8)*log(1 - 3^(1/8)*x^(1/8))/(128*x^(7/8)) + 21*3^(1/8)*log(1 - 3^(1/8)*x^(1/8)*exp_polar(pi*i))/(128*x^(7/8)) - 21*i*3^(1/8)*log(1 - 3^(1/8)*x^(1/8)*exp_polar(pi*i/2))/(128*x^(7/8)) - 21*3^(1/8)*exp(-3*pi*i/4)*log(1 - 3^(1/8)*x^(1/8)*exp_polar(5*pi*i/4))/(128*x^(7/8)) - 21*3^(1/8)*exp(-pi*i/4)*log(1 - 3^(1/8)*x^(1/8)*exp_polar(7*pi*i/4))/(128*x^(7/8)) - 21*3^(1/8)*exp(pi*i/4)*log(1 - 3^(1/8)*x^(1/8)*exp_polar(pi*i/4))/(128*x^(7/8)) - 21*3^(1/8)*exp(3*pi*i/4)*log(1 - 3^(1/8)*x^(1/8)*exp_polar(3*pi*i/4))/(128*x^(7/8)) + 21*i*3^(1/8)*log(1 - 3^(1/8)*x^(1/8)*exp_polar(3*pi*i/2))/(128*x^(7/8)))/7, 3*|x| < 1), (Sum(n*3^n*x^n/(-9 + 8*n), (n, 2, oo)), True))
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