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 CV | | if the series is convergent (to a number ∉{0,1,5‾√}∉{0,1,5}\not\in \{0, 1, \sqrt{{5}} \}) Z | | if the series converges to 0 ON | | if the series converges to 111 IN | | if the series equals to 5‾√5\sqrt{{5}} [/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 AST | | 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=3∞(−1)𝑛5−4𝑛2‾‾‾‾‾‾‾√∑n=3∞(−1)n5−4n2 \sum\limits_{n=3}^{\infty} (-1)^n\sqrt{ {5}-\frac{ {4}}{n^2} } | | because ∑𝑛=1∞(−1)𝑛ln(1+17𝑛)∑n=1∞(−1)nln⁡(1+17n) \sum\limits_{n=1}^{\infty} (-1)^n \, \ln\left(1 + \frac{{17}}{n}\right) | | because [/table]

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思路分析
To begin, I will restate the two components of the problem and then analyze each option. First series: ∑_{n=3}^{∞} (-1)^n √(5 − 4/n^2). - The general term is a_n = (-1)^n √(5 − 4/n^2). As n → ∞, √(5 − 4/n^2) → √5, so the term does not approach 0; in fact it oscillates between ±√5 asymptotically. - Because a_n does not tend to 0, ......Login to view full explanation

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