1. The problem statement, all variables and given/known data I need to find the convergence a unknown function. Now I know the Taylor series of it which is 1/3+2/(3^2)+3/(3^3+4/(4^4+...+k/(3^k). Which mean I can just take the Riemann sum of k/(3^k) from say 0 to 50 and that would give me 3/4. However this is not enough I need to confirm the answer by finding the unknown function. Normally this isnt too difficult as I would manipulate the series to get it into some sort of form that is familiar like e^x or cos(x), but this one is throwing me for a loop. The bottom part (3^k) fits x/(1-x) when x=3 but Im not sure about the top any help or hints would be great!