Vector space/Points/Barycentric combination/Exercise

Let ${}V$ be a vector space over ${}K$, which we consider as an affine space. Let ${}\sum _{i\in I}a_{i}v_{i}$ with ${}v_{i}\in V$, ${}a_{i}\in K$ and ${}\sum _{i\in I}a_{i}=1$ denote a barycentric combination. Show that the point defined by this barycentric combination in affine space equals the vector sum ${}\sum _{i\in I}a_{i}v_{i}$.

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