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Does the sum of two positive convergence series of a basic problem of advanced mathematics converge?
Absolute convergence. If it is not a positive sequence, the conclusion is also valid.

The properties of series: ∑un convergence, ∑vn convergence, then ∑ (UN VN) also converges.

Further conclusion: A and B are two non-zero numbers. If Σ UN converges and Σ VN converges, then Σ (aun+bvn) also converges.