Exponential Series Convergence

Calculus Level 2

If x1,x2,x3,x_1,x_2,x_3,\ldots is a sequence of positive reals such that k=1xk\displaystyle \sum_{k=1}^\infty x_k converges, does k=1(exk1)\sum_{k=1}^{\infty}\left(e^{x_k}-1\right) converge?

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