How do I read this triple summation? $\sum_{1\leq i < j < k \leq 4}a_{ijk}$ How do I read this triple summation? 
$$\sum_{1\leq i <  j < k \leq 4}a_{ijk}$$
The exercise asks me to express it as three sumations and to expand them in the following way:
1) Summing first on $k$, then on $j$ and last on $i$.
2) Summing first on $i$, then on $j$ and last on $k$.
My attempt:
$$
\sum_{k=3}^4\sum_{j=2}^{k-1}\sum_{i=1}^{j-1} a_{ijk}=\sum_{j=2}^2\sum_{i=1}^{j-1}a_{ij3}+\sum_{j=2}^3\sum_{i=1}^{j-1}a_{ij4}=\sum_{i=1}^1a_{i23}+\sum_{i=1}^{1}a_{i24}+\sum_{i=1}^2a_{i34}
\\=a_{123}+a_{124}+a_{134}+a_{234}$$
Is this correct so far? I don't know how to do the following parts of the exercise.
Could someone give me a general explanation on how to read this type of multiple summations?
Thanks all in advice.

You are correct.
For (1), $\displaystyle\sum_{1\leq i<j<k\leq 4}a_{ijk}=\sum_{1\leq i<j< 3}a_{ij3}+\sum_{1\leq i<j<4}a_{ij4}=\sum_{1\leq i<2}a_{i23}+\sum_{1\leq i<2}a_{i24}+\sum_{1\leq i<3}a_{i34}=a_{123}+a_{124}+a_{134}+a_{234}.$
(2) is analogous.
