oo ____ \ ` \ n \ log (2*x + 1) ) ------------- / n / 2 /___, n = 1
Sum(log(2*x + 1)^n/2^n, (n, 1, oo))
/ log(1 + 2*x) |log(1 + 2*x)| | -------------------- for -------------- < 1 | / log(1 + 2*x)\ 2 | 2*|1 - ------------| | \ 2 / | < oo | ___ | \ ` | \ -n n | / 2 *log (1 + 2*x) otherwise | /__, \n = 1
Piecewise((log(1 + 2*x)/(2*(1 - log(1 + 2*x)/2)), Abs(log(1 + 2*x))/2 < 1), (Sum(2^(-n)*log(1 + 2*x)^n, (n, 1, 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