I am trying to evaluate a fairly simple summation:


$\sum\_{k=1}^n ka^kb^{n-k}$


Which is related to the common identity for $\sum\_{k=1}^n ka^k$ available on Wikipedia.


I've previously seen lengthy lists of obscure summation formulas in the comments but could not find any this time via the search function.


I found Henry Goulds list at <https://dokumen.tips/documents/combinatorial-identities-a-standardized-set-of-tables-listing-500-binomial.html>, but it only has formulas involving binomial coefficients.


Is there a list of obscure summation identities? And in particular is there a published identity for this sum?


I got to this sum after some operations on a difference of powers factorization.



List of obscure summation identities
As suggested by the OP, I post my comment as an answer:


Try out Wolfram Alpha. The code for your example is <https://www.wolframalpha.com/input/?i=Sum%5B+k+a+%5Ek+b%5E%28n-k%29+%2C+%7B+k%2C+1%2C+n+%7D+%5D>


