📝 题目
4. 1.3 判断下列级数的收敛性:
(1) $\displaystyle{\mathop{\sum }\limits_{{n = 1}}^{\infty }\frac{1}{{2}^{\ln n}}}$ (2) $\displaystyle{\mathop{\sum }\limits_{{n = 1}}^{\infty }\frac{1}{{n}^{\ln n}}}$
(3) $\displaystyle{\mathop{\sum }\limits_{{n = 1}}^{\infty }\frac{n}{{3}^{\sqrt{n}}}}$ (4) $\mathop{\sum }\limits_{{n = 2}}^{\infty }\frac{\ln n}{{n}^{p}}\left( {p > 1}\right)$ .
💡 答案与解析
4.1.3 (1)发散；(2)收敛；(3)收敛；(4)收敛.