I want ask Mathematica at wolframalpha for …
\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)*
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.
seanc
March 16, 2014, 10:41pm
3
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.
Unless I made a mistake Mathematica can’t do this either.
@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…
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 !
