Math 141 Quiz 7 Problems

1. Determine whether or not the alternating series converge or diverge.
(a)
( 1) n 1

n ln n 1
1

(b)


( 1) n

n
1

2n 2 n 2
5n 2 2n 1

2. Determine whether the series converges absolutely, or converges conditionally, or
diverges and give reasons for your conclusions.
(a)
( 1) n

n 3n 4
1

(b)



( 0.2) n

n
1

3. Use Ratio Test or Root Test to determine whether the following infinite series are
absolutely convergent.
(a)

2n
( 1) n 1 2

n
n
1

(b)
2 
ln n 

n 
2


n

4. Calculate the Maclaurin series for

1
f ( x) 
2x

to the

term.
x3

5. Find the interval of convergence for the power series
(a)

1

x n 1
n 2n 1
1

(b)

n n
x
n
n 2
1




6. Use substitution method and a known power series to find power series for
. Please express your answer in sigma notation.
f ( x) x cos(3 x )