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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §10.3 Convergence Tests: All Series, #38 · Calculus · Series

True or false: (a) Every alternating series converges

True or false:
(a) Every alternating series converges.
(b) $Σ a_{n}$ converges conditionally if $Σ∣ a_{n} ∣$ diverges.
(c) A convergent series with positive terms is absolutely convergent.
(d) If $Σ a_{n}$ and $Σ b_{n}$ both converge, so does $Σ (a_{n} + b_{n})$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §10.3 Convergence Tests: All Series, #38

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