題目 Problem Part I Multiple Choice (A) ∑n=1∞(−1)n(1−cos1n)\sum_{n=1}^\infty (-1)^n\left(1-\cos\dfrac{1}{n}\right)∑n=1∞(−1)n(1−cosn1) is absolutely convergent. (B) ∑n=1∞1n−lnn\sum_{n=1}^\infty \dfrac{1}{n-\ln n}∑n=1∞n−lnn1 is convergent. (C) ∑n=1∞1n1+1n\sum_{n=1}^\infty \dfrac{1}{n^{1+\frac{1}{n}}}∑n=1∞n1+n11 is convergent. (D) ∑n=2∞1nln(n+1n−1)\sum_{n=2}^\infty \dfrac{1}{n}\ln\left(\dfrac{n+1}{n-1}\right)∑n=2∞n1ln(n−1n+1) is divergent. 解答
