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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §10.3 Convergence Tests: All Series, #33 · Calculus · Series

If … and … are convergent show that … is absolutely convergent

If $Σ a_{n}^{2}$ and $Σ b_{n}^{2}$ are convergent show that $Σ a_{n} b_{n}$ is absolutely convergent.
Hint: $(a \pm b)^{2} \geq 0$ yields $2∣ ab ∣ \leq a^{2} + b^{2}$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §10.3 Convergence Tests: All Series, #33

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