Consider two series \({S_1} = \mathop \sum \limits_{n = 1}^\infty {a_n}\) and \({S_2} = \mathop \sum \limits_{n = 1}^\infty {b_n}\) where \({a_n} = \frac{1}{n}\sin \frac{1}{n}\) and \({b_n} = \frac{1}{{{n^2}}}\), then
1
Both S1 and S2 are convergent
2
S1 is convergent and S2 is divergent
3
Both S1 and S2 are divergent
4
S1 is divergent and S2 is convergent