I apologize if the title is incorrect, I am not exactly sure how to describe this. I am trying to solve a summation: $$ \sum_{k=0}^n{3^{-k}7^{n-k}} $$ I am not sure how I would go about solving this. I considered distributing the summation to each term but using wolfram gave me different answers. Either way I do not want to rely on calculators to solve sums like these. How can I go about solving a sum like this?
And in general, is there a place I can read more about summation properties?
Thank you