1. The problem statement, all variables and given/known data http://latex.codecogs.com/examples/00a93bb6c6c645f9802b88f4c1c986fc.gif [Broken] Let's call this L. Find the exact value of L. 2. Relevant equations http://latex.codecogs.com/examples/6835d744da9ce19b352158cd01b91e91.gif [Broken] 1+1/2=1,5 3. The attempt at a solution L>0. 1,5>L The function is always growing Therefore there must be an definite answer in ]1,5 ; 0[ Wolfram gives 1,291286... Spam of possible methods: -Trying to find the value relating it to integration. Impossible. The integral is not defined. -Try to find an adequate Taylor Expansion. Can't find a function that fits AND I don't know any pretty method to relation expansions to functions. -Try to find a relatable sum such as that of the differences or quocients of the next term. Couldn't do much with it. -Use n^-n=e^ln(n^-n)=e^(-n*ln n). Can't do much with it. -Turn into a product problem n^-n=ln(e^(n^-n)). Can't do much with it. -Use a general formula for the sum of a^(k) to infinity. Haven't tried but it doesn't seem to simplify. Main question: Is it representable using already known constants?