MATH 152 Activity 12 (Section 10.5-10.6)
Directions: Put both your name and your partners name on the answersheet. Use scratch paper for work, meaning only
put the answers on the answer sheet. Turn in only ONE answer sheet per pair. Calculators are allowed and you may
use your notes and textbook. Failure to follow these instructions will result in a 1 point deduction. Neat handwriting is
expected.
1. Find the radius and interval of convergence for the series
∞
X
(4x − 1)n
n+1
n=2
2. Find the radius and interval of convergence for the series
∞
X
(5x + 2)n
(n + 1)!
n=0
3. Find the radius of convergence for the series
4. Suppose it is known that
∞
P
∞
X
xn n!
10n
n=1
cn (x − 1)n converges when x = 2. On what interval are we guaranteed convergence?
n=0
5. Express f (x) =
1
as a power series.
1 + 4x2
6. Express f (x) =
1
as a power series.
(1 − 8x)2
7. Express f (x) = ln(x2 + 2) as a power series.
Z 0.5
1
8. Evaluate
dx as a series.
1
+
x5
0
1