Problem
|
Answer
|
Comment
|
| 23 |
True |
The full geometric series with a=1/3 and r=1/3 has sum 1/2. |
| 24 |
False |
This is true if you know the terms are positive. (see #26) |
| 26 |
True |
(see #24) |
| 28 |
True |
|
| 29 |
True |
Converges at x=-1.1 means radius of convergence is at least 3-(-1.1)=4.1. Since 7-3=4<4.1, the series must converge here as well. |
| 30 |
False |
Converges at x=-2 means radius of convergence is at least 0-(-2)=2. Since 2-0=2, there is no guarantee that the series converges here. (If x=-2 is an endpoint for the interval of convergence, then x=2 is the other endpoint. |
| 31 |
True |
|
| 32 |
False |
Every power series converges for at least one value of the variable. |