Is there a closed form solution to this infinite series?
x is a number between 0 and 1.
n can take any value between 1 and infinity.
1/n + x/(n+2) + x^2/(n+4) + x^3/(n+6) + ...................
Thanks!
Let's suppose that n is a 'natural number' so that we have a family of functions defined as...
(1)
First we set and then we start with n=1…
(1)
Now for n=2...
(2)
Now for n=3...
(3)
And now for n=4...
(4)
Observing (1), (2), (3) and (4) it seems that the general explicit expression for is...
(5)
Kind regards
P.S. : also the expressions like can be written as functions of x...