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How to ask Wolfram alpha for this limit?

Posted 11 years ago
I want ask Mathematica at wolframalpha for ...
   (sorry: I had formatted it in Mathjax, so I take a screenshot for my question here)

$$ \lim_{n \to \infty} \exp(x \cdot (n+1)) \sum_{k=0}^n \left( (n+1-k)^k {(-x \exp(-x))^k \over k! }\right) $$
and put it in various notation styles, one of them     

    Limit [ exp(x*(n+1)) * sum[ (n+1-k)^k *((-x) *exp(-x))^k/k!, k=0 to n], n -> infinity]

but WA always complains it cannot understand...    

***Q:*** What am I doing wrong?        

*(If I ask partial expressions from this it* **can** *understand them)* 
POSTED BY: Gottfried Helms
5 Replies
Posted 11 years ago
Even when you make x=1/d where d is a nonzero integer and the limit seems clear it does not seem to be able to find a solution.
POSTED BY: Bill Simpson
Wolfram|Alpha limits the size and complexity of the inputs it will handle. Additionally, it does not always accept Mathematica syntax. 

For more complicated problems like this one, you'll want to try using Mathematica itself. 
POSTED BY: Sean Clarke
Posted 11 years ago
Unless I made a mistake Mathematica can't do this either.
POSTED BY: Bill Simpson
@Sean - unfortunately it doesn't say so; it would be better it would say "too complicated" so I knew it is not a question of syntax-error. But well...
POSTED BY: Gottfried Helms
Just for the record: the solution is the geometric series in x, applicable for x from - infinity to 1 (exclusively); it's just a matrix-summation-method.      

So I do know now what was happening - many thanks for your answers/help !
POSTED BY: Gottfried Helms
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