Help with a question on convolution?

Question

I need help solving this convolution question for an assignment.

I need to find the convolution of the two functions.

I've searched online for a way to approach this question, but this was the most helpful thing I could find:

http://www.ee.ic.ac.uk/hp/staff/dmb/courses/E1Fourier/00700_TransformParseval.pdf

But that works with integrals instead of sums and the required answer I'm supposed to get is:

Answer 1

Use the convolution theorem (convolution in the time domain is equivalent to multiplication in the frequency domain) and then inverse Fourier Transform (tables if you are allowed, although applying the definition is just as easy and the result you are looking for is the Fourier Transform pair between a Dirac Delta and a Complex Exponential).