Writing Single summation with two variables

Question

I have the following summation,

What its the mathematically correct way to write this summation using the summation symbol? Note that I will need 2 variables.

Answer 1

You have

$$\sum_{i=1}^{N-t}A_{t+i}(k-i)\;.$$

This can also be written

$$\sum_{i=t+1}^NA_i(k+t-i)\;.$$

Answer 2

Here is one way to write it: $$ \sum_{j=1}^{N-t}A_{t+j}(k-j) $$