Alec, this seems to work! great!

thank you very much!! :D

The other sums suggested by RobertIsrael gave me the same result (actually I started from those, since i am computing Bose-Einstein condensation for a finite number of particles)

Ok i tried with fsolve for now;

seems to work with some constraints, but with my ones

N=1000

c=0.005

it doesn't work for x=1

if i put c= 0.001 it works until x<0.6 then it doesn't...this is enough anyway, i am interested in values near x=1

Now the problem...how do i plot it in function of x ? this way it doesn't accept a command like:

plot(Z(x,1000,0.001),x=0.6..1.1) because "x in the equation, and it is not solved for" 

how do i tell him that x is a variable?or perhaps i could make a plot value-by value,point by point... but how?I need lots of points :)

i am sorry, i written the wrong expression... j does multiply the constant c in the exp() function...

solve( N=sum(  z^j / (1-exp(-jc / x)) ,j=1..infinity), z);

this way doesn't work.