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msc:mcqs_short_questions:real_analysis [2023/04/03 04:03] – [Sequence of Numbers] Administratormsc:mcqs_short_questions:real_analysis [2023/04/03 04:06] (current) – [Series of Numbers] Administrator
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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="link" collapse="310">See Answer</btn><collapse id="310" collapsed="true">(C): It is definition of absolutely convergent. </collapse>     * (D) $\sum |a_n|$ is divergent but $\sum a_n$ is convergent. \\ <btn type="link" collapse="310">See Answer</btn><collapse id="310" collapsed="true">(C): It is definition of absolutely convergent. </collapse>
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 +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="link" collapse="311">See Answer</btn><collapse id="311" collapsed="true">(B): By definition, a series is convergent if its sequence of partial sum is convergent.</collapse>
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 ==== Limit of functions ==== ==== Limit of functions ====