How to write an expression using sigma notations?

Question

If I have $4^{n-1}*6+4^{n-2}*6+4^{n-3}*6+...+4*6 + 6$ how do I rewrite such expression as sum notation? I do know the answer, I don't really understand how to go from this expression and make a sigma notation?

Answer 1

You have terms of the form $4^i\times 6$, where $i$ starts from $n-1$ and finishes at $0$. In notation, $$\sum_{i=0}^{n-1} 4^i\times 6,$$ or, equivalently, $6 \sum_{i=0}^{n-1}4^i$.