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### prove an identity for any integer

Let $n$ be a positive integer and $m = (m_1, \ldots, m_n)$ an $n$-dimensional vector of real numbers. Let $g$ be a real number.

I want to prove, for any $n$ and $m$, an equality of the form $$\sum_{i=1}^n f_i (m,g) = 0$$ where the function $f_i$ is a rational function of $m$ and $g$.

Of course it's easy to check this by substituting finite values of $n$, but is there a way in Sage to prove it for any integer?