algebraic sums of reciprocals Re: a 3^N - 2^N - related series.

[Ralf Stephan]

>  Consider the following series:
> 
>                 __ oo
>                 \                   1
>        f(N) = -  >       ------------------------
>                 /_        (i*2^N - 1)((i+1)*2^N-1)
>                    i=0

I think this is one of the many special cases of the theorems in

H. Hu, Z.-W. Sun and J.-X. Liu, <a href="http://pweb.nju.edu.cn/zwsun/39f.pdf">Reciprocal sums of second order recurrent sequences</a>, Fib. Quart. 39(2001), no. 3, 214-220.

I think they have succeeded in collecting all cases of algebraic sums
of reciprocals of integer sequences but I am not 100 per cent sure.


Regards,
ralf