Question: What means "try the front-end to compute simple definite sums"?

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?

Thanks for help, i really need to know,

Tim

The exact input and output is used:

> infolevel[all]:=5:simplify(sum( i*binomial(k,i) / (k-1)^i  , i=0..k ));

sum:   "process the input arguments"

sum:   "definite sum"

Standard:   "try the front-end to compute simple definite sums"

simplify/do:   applying  commonpow  function to expression

simplify/do:   applying  power  function to expression

                               /  k  \k

                               |-----|

                               \k - 1/