Can I use this formula to simplify my summations?

[Luongo]

1. on #1 c) of the homework:
http://www.math.ubc.ca/~oyilmaz/courses/m267/hmk3.pdf
how do i multiply this summation?

Homework Equations

3. what i did was i multiplied the 2 expos and made on of the k indexes a 'm' instead and i got $$\sum e^i(k+m)t$$

 

[praharmitra]

$$\left( \sum_{k =1}^{N_1} f(k) \right) \left( \sum_{j=1}^{N_2} g(j) \right) = \sum_{k=1}^{N_1} \sum_{j=1}^{N_2} f(k)g(j)$$

Can you try to see why the above is true?

Now in your problem, k is a dummy variable (meaning, that since it sums over, it doesn't matter if we call it k, or j). So we can replace the variable in the second summation, by j. Then you can apply the above formula.