Rearrange convergent series

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It was long time ago I studied analyze and I do have forgot a lot, but isn't it so that any convergent series $$\sum_{i=1}^\infty a_i$$ can be rearranged to an absolut convergent series $$\sum_{i=1}^\infty \left|\sum_{j=1}^{n_i} b_{ij}\right|=\sum_{k=1}^\infty a_k$$ where the $b_{ij}$-s is a rearrangement of the $a_k$-s?