Q11·Section A (Section A)·11 of 60Absolute convergence of two trigonometric seriesFor n∈Nn\in\mathbb{N}n∈N, let an=nsin2(1n)cosna_n=\sqrt{n}\sin^2\bigl(\frac1n\bigr)\cos nan=nsin2(n1)cosn, and bn=nsin(1n2)cosnb_n=\sqrt{n}\sin\bigl(\frac1{n^2}\bigr)\cos nbn=nsin(n21)cosn. Then OptionsAthe series ∑n=1∞an\sum_{n=1}^\infty a_n∑n=1∞an converges but the series ∑n=1∞bn\sum_{n=1}^\infty b_n∑n=1∞bn does NOT convergeBthe series ∑n=1∞an\sum_{n=1}^\infty a_n∑n=1∞an does NOT converge but the series ∑n=1∞bn\sum_{n=1}^\infty b_n∑n=1∞bn convergesCboth the series ∑n=1∞an\sum_{n=1}^\infty a_n∑n=1∞an and ∑n=1∞bn\sum_{n=1}^\infty b_n∑n=1∞bn convergeDneither the series ∑n=1∞an\sum_{n=1}^\infty a_n∑n=1∞an nor the series ∑n=1∞bn\sum_{n=1}^\infty b_n∑n=1∞bn convergesPick an option to check your answer.Show answerShow solution Report a problem with this question← Q10All questionsQ12 →Keyboard: A–D answer · S solution · ←/→ previous/next