Exponential Series Convergence

Calculus Level 2

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

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