Vector space/General distributivity law/Exercise

Let $V$ be a vector space over a field $K$. Let $s_1,\dots ,s_k\in K$ and $v_1,\dots ,v_n\in V$. Show

$\left(\sum _{i=1}^k{s}_i\right)\cdot \left(\sum _{j=1}^n{v}_j\right)=\sum _{1\le i\le k,1\le j\le n}{s}_i\cdot v_j.$

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