题目
题目
多项填空题

Question textFor each of the series below you find two answer fields. In the first answer field enter: (inputs are case sensitive) [table] DV | | if the series is divergent and not equal to ±∞±∞\pm\infty CV | | if the series is convergent (to a non-zero number) Z | | if the series converges to 0 INF | | if the series equals to ∞∞ \infty NIF | | if the series equals to −∞−∞ -\infty [/table] [table] WD | | if the series is not well defined | | [/table] In the second answer field select one of the following reasons that can be used to prove your claim in the first answer field: [table] DT | | The Divergency Test IT | | The Integral Test AS | | The Alternating Series Test RO | | The Root Test RA | | The Ratio Test [/table] [table] D | | The sequence of summands decreases to 00 0 L | | The limit of summands exists and equals to 00 0 C | | Comparison with a  geometric series ∑∞𝑛=0𝑞𝑛∑n=0∞qn \sum_{n=0}^{\infty}q^n CH | | Comparison with the harmonic series AH | | Comparison with the alternating harmonic series [/table] [table] P | | Comparison with 𝑝pp-series, where 𝑝>1p>1p > 1 LP | | Comparison with 𝑝pp-series, where 𝑝<1p<1p < 1 [/table] [table] ∑𝑛=1∞sin(𝜋9𝑛)∑n=1∞sin⁡(π9n) \sum_{n=1}^\infty \sin\left( \frac{\pi }{ {9} n } \right) | | because ∑𝑛=1∞cos(𝜋10𝑛)∑n=1∞cos⁡(π10n) \sum\limits_{n=1}^{\infty} \cos\left( \frac{\pi }{ {10} n } \right) | | because [/table]

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思路分析
Question restatement and options: - In the first answer field enter the category for the series: DV, CV, Z, INF, NIF, WD, with the second field selecting a justification from DT, IT, AS, RO, RA, followed by a second pair of selections (D, L, C, CH, AH, P, LP) and finally two target series to classify. - For the given response, the first blank is INF and the second blank is INF, with the reasons provided as CH and DT respectively. Analysis of the first claim: INF because CH - The statement INF indicates the series diverges to infinity. A common approach to justify this is by a Comparison with a geometric-like or harmonic-like divergent benchma......Login to view full explanation

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