Name:
Quiz #7 (8.3-8.6); Score: (10, 8, 6, or 2) points
Closed book, no notes, no neighbors, no calculators.
MATH 232-005
Fall 2025
1. Use the Integral Test to determine if the following series is absolutely convergent,
conditionally convergent, or divergent.
∞
∑
2n
2
n=1 n + 5
2. Determine whether the series is absolutely convergent, conditionally convergent, or
divergent. Be sure to state which test(s) you use.
∞
∑
(−1)n
√
(a)
n+7
n=1
(b)
∞
∑
(−1)n 8 n
n3 + 4
n=1
3. Write 1 or 2 sentences for each part.
(a) Distinguish between Absolutely Convergent and Conditionally Convergent.
(b) Why do we use the Ratio Test to determine the Interval of Convergence?
4. Find the radius of convergence and state the interval of convergence for each series.
(a)
∞
∑
n=1
(b)
∞
∑
n=1
(x + 2)n
(n + 1) 3n
(x + 6)n
(3n)!
5. Use your favorite power series function to create a power series representation of
f (x) = ln(5 + x)