Consider two series \(\mathop \sum \limits_{n = 1}^\infty {a_n}\) and \(\mathop \sum \limits_{n = 1}^\infty {b_n}\) where \({a_n} = \frac{1}{{n\sqrt n }}\) and \({b_n} = \frac{1}{{n!}}\), then
1
The series \(\mathop \sum \limits_{n = 1}^\infty {a_n}\) is convergent and \(\mathop \sum \limits_{n = 1}^\infty {b_n}\) is divergent.
2
The series \(\mathop \sum \limits_{n = 1}^\infty {a_n}\) is divergent and \(\mathop \sum \limits_{n = 1}^\infty {b_n}\) is convergent.
3
Both the series \(\mathop \sum \limits_{n = 1}^\infty {a_n}\) and \(\mathop \sum \limits_{n = 1}^\infty {b_n}\) are divergent.
4
Both the series \(\mathop \sum \limits_{n = 1}^\infty {a_n}\) and \(\mathop \sum \limits_{n = 1}^\infty {b_n}\) are convergent.