Maple transforms the sum

sum( i*binomial(k,i) / (k-1)^i  , i=0..k )

to

(k/(k-1))^k,

which converges to e. The exact input and output is listed below. However, how does this surprising transformation work? I tried to use the infolevel command to see what actually happens as shown below. Is something wrong with my use of the infolevel command? Does maybe "definite sum" mean that this is a predefined sum in maple? In this case, is there a possibility to list this sum or to get a reference to an external document?