You're definitely on the right track, nice work!
There is some confusion, because you've used the same index to represent both the original summation and the summation needed for Since the i index is used in the orginal summation, we would want to use a new dummy index, e.g. write
Then the double summation is a summation over the indices i and j.
Does this help? I can write up more details if it's still confusing.