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| Both sides previous revision Previous revision Next revision | Previous revision | ||
| msc:mcqs_short_questions:real_analysis [2023/04/03 03:59] – [Edit - Panel] Administrator | msc:mcqs_short_questions:real_analysis [2023/04/03 04:06] (current) – [Series of Numbers] Administrator | ||
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| Line 43: | Line 43: | ||
| * (B) 2 | * (B) 2 | ||
| * (C) $2n$ such that $n \in \mathbb{Z}$ | * (C) $2n$ such that $n \in \mathbb{Z}$ | ||
| - | * (D) $2\pi$ \\ <btn type=" | + | * (D) $2\pi$ \\ <btn type=" |
| - | </ | + | </ |
| + | < | ||
| 4. A number which is neither positive nor negative is | 4. A number which is neither positive nor negative is | ||
| * (A) 0 | * (A) 0 | ||
| Line 168: | Line 169: | ||
| * (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 ==== | ||
| Line 238: | Line 233: | ||
| * (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 ==== | ||