Summation Notation Confusion I am unclear about what the following summation means given that $\lambda_i: \forall i \in \{1,2,\ldots n\}$:
$\mu_{4:4} = \sum\limits_{i=1}^{4} \lambda_i + \mathop{\sum\sum}_{1\leq i_1 < i_2 \leq 4}(\lambda_{i_1} + \lambda_{i_2}) + \mathop{\sum\sum\sum}_{1\leq i_1 < i_2 <i_3 \leq 4}(\lambda_{i_1} + \lambda_{i_2} + \lambda_{i_3})$
I understand how this term expands:
$\sum\limits_{i=1}^{4} \lambda_i = \lambda_1 + \lambda_2 + \lambda_3 + \lambda_4$.
But, I don't understand what how this term expands
$\mathop{\sum\sum}_{\substack{1\leq i_1 < i_2 \leq 4}}(\lambda_{i_1} + \lambda_{i_2})$
Nor do I understand how this term expands
$\mathop{\sum\sum\sum}_{\substack{1\leq i_1 < i_2 <i_3 \leq 4}}(\lambda_{i_1} + \lambda_{i_2} + \lambda_{i_3})
$
Any help in these matters would be appreciated.

I would interpret ${\sum\sum}_{\substack{1\leq i_1<i_2\leq 4}}(\lambda_{i_1}+\lambda_{i_2})$ as $(\lambda_1+\lambda_2)+(\lambda_1+\lambda_3)+(\lambda_1+\lambda_4)+(\lambda_2+\lambda_3)+(\lambda_2+\lambda_4)+(\lambda_3+\lambda_4)$
I would interpret ${\sum\sum\sum}_{\substack{1\leq i_1 < i_2 <i_3 \leq 4}}(\lambda_{i_1}+\lambda_{i_2}+\lambda_{i_3})$ as $(\lambda_1+\lambda_2+\lambda_3)+(\lambda_1+\lambda_2+\lambda_4)+(\lambda_1+\lambda_3+\lambda_4)+(\lambda_2+\lambda_3+\lambda_4)$
