I.If a new series is found by integrating a known series with included endpoints
ID: 2895590 • Letter: I
Question
I.If a new series is found by integrating a known series with included endpoints, those endpoints might not be included in the new series.
II.If a new series is found by integrating a known series with included endpoints, those endpoints will never be included in the new series.
III.If a new series is found by integrating a known series with included endpoints, the endpoints in the new series will also be included.
a) I only
b) II only
c) III only
d) None of these statements are true.
Which of the following statements are true? (4 points)I.If a new series is found by integrating a known series with included endpoints, those endpoints might not be included in the new series.
II.If a new series is found by integrating a known series with included endpoints, those endpoints will never be included in the new series.
III.If a new series is found by integrating a known series with included endpoints, the endpoints in the new series will also be included.
a) I only
b) II only
c) III only
d) None of these statements are true.
Explanation / Answer
option a) is correct
in case of integration,
If a power series is integrated, then the integrated series has the same interval of convergent as the original series EXCEPT possibly the gain of one or both end points of the interval of convergence if the original series wasn't convergent at the end points already.