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Convergence of the series at the endpoints, $x=\\pm 1$, depends on the values of $\\alpha$ and needs to be checked in every concrete case. In this note, using new approach, we reprove the convergence of the hypergeometric series $_{2}F_{1}(\\alpha,\\beta;\\beta;x)$ for $|x|<1$ and obtain new result on its convergence at point $x=-1$ for every integer $\\alpha\\neq 0$. 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