MCQOPTIONS
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MCQOPTIONS
This section includes 8 Mcqs, each offering curated multiple-choice questions to sharpen your Discrete Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Determine the radius of convergence and interval of convergence for the power series: n=0 (x 7)n+1/nn. |
| A. | 0, 1<x<1 |
| B. | , <x< |
| C. | 1, 2<x<2 |
| D. | 2, 1<x<1 |
| Answer» C. 1, 2<x<2 | |
| 2. |
What is the radius of convergence and interval of convergence for the power series n=0m!(2x-1)m? |
| A. | 3, 12 |
| B. | 1, 0.87 |
| C. | 2, 5.4 |
| D. | 0, 1/2 |
| Answer» E. | |
| 3. |
Find the power series representation for the function f(x)=x/4 x. |
| A. | <sub>n=0</sub>x<sup>n+1</sup>/4<sup>n+1</sup> |
| B. | <sub>n=0</sub>x<sup>n+1</sup>4<sup>n</sup> |
| C. | <sub>n=0</sub>x<sup>n</sup>4<sup>n</sup> |
| D. | <sub>n=0</sub>x<sup>n+1</sup> |
| Answer» B. <sub>n=0</sub>x<sup>n+1</sup>4<sup>n</sup> | |
| 4. |
Determine a power series representation for the function g(x)=ln(7 x). |
| A. | <sub>n</sub>=0 x<sup>n+1</sup>/7<sup>n+1</sup> |
| B. | ln(14) <sub>n</sub>=0 x<sup>n+1</sup>/7n |
| C. | ln(7) <sub>n</sub>=0 x<sup>n+1</sup>/7<sup>n+1</sup> |
| D. | ln <sub>n</sub>=0 x/7<sup>n+1</sup> |
| Answer» D. ln <sub>n</sub>=0 x/7<sup>n+1</sup> | |
| 5. |
Determine the interval and radius of convergence for the power series: n=17n/n(3x 1)n-1. |
| A. | (2x+1)/6 |
| B. | 7|3x 1| |
| C. | 5|x+1| |
| D. | 3!*|4x 9| |
| Answer» C. 5|x+1| | |
| 6. |
Which of the following series is called the formal power series ? |
| A. | b<sub>0</sub>+b<sub>1</sub>x+b<sub>2</sub>x<sup>2</sup>+ +b<sub>n</sub>x<sup>n</sup> |
| B. | b<sub>1</sub>x+b<sub>2</sub>x<sup>2</sup>+ +b<sub>n</sub>x<sup>n</sup> |
| C. | 1/2b<sub>0</sub>+1/3b<sub>1</sub>x+1/4b<sub>2</sub>x<sup>2</sup>+ +1/nb<sub>n</sub>x<sup>n</sup> |
| D. | n<sup>2</sup>(b<sub>0</sub>+b<sub>1</sub>x+b<sub>2</sub>x<sup>2</sup>+ +b<sub>n</sub>x<sup>n</sup>) |
| Answer» B. b<sub>1</sub>x+b<sub>2</sub>x<sup>2</sup>+ +b<sub>n</sub>x<sup>n</sup> | |
| 7. |
The third term of a geometric progression with common ratio equal to half the initial term is 81. Determine the 12th term. |
| A. | 3<sup>12</sup> |
| B. | 4<sup>15</sup> |
| C. | 6<sup>8</sup> |
| D. | 5<sup>9</sup> |
| Answer» B. 4<sup>15</sup> | |
| 8. |
The explicit formula for the geometric sequence 3, 15, 75, 375, is _______ |
| A. | 2*6! * 3<sup>n-1</sup> |
| B. | 3 * 5<sup>n-1</sup> |
| C. | 3! * 8<sup>n-1</sup> |
| D. | 7 * 4<sup>n-1</sup> |
| Answer» C. 3! * 8<sup>n-1</sup> | |