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Chapter 02 - Sequence and Series

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itive integer such that $\left| {\,{s_n}}\right|>\frac{1}{2}s$. * Theorem: Let //a// and //b// be fixe... _n}{t_n}\right\}$ converges to st. (iii) $\left\{\frac{{{s_n}}}{{{t_n}}} \right\}$ converges to $\frac{s}{t}$ provided ${t_n}\ne 0\,\,\,\,\forall \,\,\,n$ and... orem: Let $a_n>0, b_n>0$ and $\lim_{n\to\infty } \frac{a_n}{b_n}=\lambda\ne 0$ then the series $\sum{a_n