# Infinite Sum using $x^{-x}$ [duplicate]

How can I calculate the value of the infinite sum $$\sum_{x=1}^\infty x^{-x}$$ By comparison to a geometric series, I know that it converges, but I don't know how to calculate an exact value. So far I have tried the following:

• I have tried to turn it into a telescoping sum, but have had no luck

• I tried adding a variable and differentiating it to create an easier sum

Any hints?