Can we multiply two sums? Yes, you can multiply two sums according to distributive law for multiplication.

Can you multiply sigma notation?

Sigma notation is essentially a shortcut way to show addition of series or sequences of numbers. It's based on the upper case Greek letter S, which indicates a sum. If the series is multiplied by a constant, you can find the sum of the series, then multiply the answer by the constant.

Can you split up summations?

Splitting summations

One way to obtain bounds on a difficult summation is to express the series as the sum of two or more series by partitioning the range of the index and then to bound each of the resulting series.