Skip to content
free
K
1
2
practice
Home
Math
English
Science
Social Studies
Contact
Language
English
Español
Sign In
/
Math
/
Calculus II
/
Endpoint Testing for Power Series
Worksheet
Grade Level
Calculus II
CAL2.138 Endpoint Testing for Power Series
0%
Skill Level
🔴 Hard
00:00
Progress to Next Level
25% to Medium
Easy
Medium
Hard
Mastery
100%
For S(x) = Σ_{n=1}^∞ [sqrt(n)/(n
2
+ 1)]((x + 7)/2)
n
, endpoint substitution gives boundary series at x = -9 and x = -5. Which option uses the correct endpoint tests and conclusions?
A
At both endpoints, the ratio test gives a limit less than 1, so both endpoints converge automatically.
B
At x = -9, converges absolutely by limit comparison with 1/n^(3/2); at x = -5, converges absolutely by limit comparison with 1/n^(3/2).
C
At x = -9, ignore the sign and use only the positive-series test; at x = -5, do the same.
D
Both endpoints diverge because the ratio test is inconclusive when its limit equals 1.
Submit Answer
