Help me to understand the summation notation

Question

I am having following expression, limits of summations are given in terms of set, can someone help me to interpret this summation. where $d_{1}$ and $d_{2}$ are distances.

$$\sum_{i_1,i_2 \in \{1,2\}} d_{i_1} e^{-d_{i_1}} * d_{i_2} e^{-d_{i_2}}$$

Answer 1

It's $$\sum_{i_1,i_2\in \{1,2\}}d_{i_1}e^{-d_{i_1}}d_{i_2}e^{-d_{i_2}}$$ $$=d_1e^{-d_1}d_1e^{-d_1}+d_1e^{-d_1}d_2e^{-d_2}+d_2e^{-d_2}d_1e^{-d_1}+d_2e^{-d_2}d_2e^{-d_2}$$ $$=d_1^2e^{-2d_1}+2d_1e^{-d_1}d_2e^{-d_2}+d_2e^{-2d_2}$$ $$=(d_1e^{-d_1}+d_2e^{-d_2})^2$$