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msc:mcqs_short_questions:real_analysis [2023/04/03 04:02] – [Edit - Panel] Administrator | msc:mcqs_short_questions:real_analysis [2023/04/03 04:06] (current) – [Series of Numbers] Administrator | ||
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* (C) is convergent. | * (C) is convergent. | ||
* (D) is divergent. \\ <btn type=" | * (D) is divergent. \\ <btn type=" | ||
- | </ | ||
- | - A series $\sum a_n$ is convergent if and only if ..................... is convergent | ||
- | * (A) $\{\sum_{k=1}^{\infty}a_k \}$ | ||
- | * (B) $\{\sum_{k=1}^{n}a_k \}$ | ||
- | * (C) $\{\sum_{n=1}^{\infty}a_k \}$ | ||
- | * (D) $\{ a_n \}$ \\ <btn type=" | ||
</ | </ | ||
==== Series of Numbers ==== | ==== Series of Numbers ==== | ||
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* (C) $\sum |a_n|$ is convergent. | * (C) $\sum |a_n|$ is convergent. | ||
* (D) $\sum |a_n|$ is divergent but $\sum a_n$ is convergent. \\ <btn type=" | * (D) $\sum |a_n|$ is divergent but $\sum a_n$ is convergent. \\ <btn type=" | ||
+ | </ | ||
+ | 11. A series $\sum a_n$ is convergent if and only if ..................... is convergent | ||
+ | * (A) $\{\sum_{k=1}^{\infty}a_k \}$ | ||
+ | * (B) $\{\sum_{k=1}^{n}a_k \}$ | ||
+ | * (C) $\{\sum_{n=1}^{\infty}a_k \}$ | ||
+ | * (D) $\{ a_n \}$ \\ <btn type=" | ||
</ | </ | ||
==== Limit of functions ==== | ==== Limit of functions ==== |