Scribd
Upload
20 views5 pages

Midterm1 Practice

Uploaded by

thunma2010
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
20 views5 pages

Midterm1 Practice

Uploaded by

thunma2010
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 5

MAT 127 MIDTERM I

PRACTICE PROBLEMS

1. Determine whether the following sequences converge or diverge.


(a) (10 pts)
2n3 + n − 1
an = 3
4n + n2 + n − 1

(b) (10 pts)


2n + sin(n)
an =
n!
Practice midterm I MAT 127

2. Determine whether the following series converge or diverge.


(a) (10 pts)
∑∞ ( )
1 7n
+
n=1
n2 6n+1

(b) (10 pts)


∞
∑ (−1)n
n=1
2n − 1
Practice midterm I MAT 127

∞
∑ 1
3. (20 pts) Is the series convergent or divergent? [Hint: Use the integral test and
n=2
n log n
note the starting point of the series.]
Practice midterm I MAT 127

4. Find the radius and interval of convergence of the following power series.
(a) (10 pts)
∑∞
(−1)n (3x)n
n=1
n!

(b) (10 pts)


∞
∑ (x − 1)n
√
n=1
n
Practice midterm I MAT 127

5. Find a power series representation of the following functions. Also determine the interval of
convergence.
2
(a) (10 pts) f (x) =
3 + x2

( )
(b) (10 pts) g(x) = √2 arctan √x [Hint: What is the derivative of g(x)?]
3 3

You might also like