I would like to use a non-algorithmic notation to denote an iteration that stores the scalar values of all summations say, for $p=1,\dotsc,3$ in a vector $v$.
This is the general notation: $\sum_{j=1}^{p}a_{j}=a_1+a_2+\dotsb+a_p$, consider $a\in \mathbb{R}$, and then: \begin{align} v_1&=\sum_{j=1}^{1}a_{j}=a_1 \\ v_2&=\sum_{j=1}^{2}a_{j}=a_1+a_2 \\ v_3&=\sum_{j=1}^{3}a_{j}=a_1+a_2+a_3 \\ \end{align}
So that I get $v=(v_1,v_2,v_3)^T$. I think that $v_p=\sum_{j=1}^{p}a_{j}$ will not suffice and it is not clear. What I should use?