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BC Calculus - Series Assessment

Total questions: 10

Worksheet time: 23mins

Name
Class
Date
1.

Determine whether the series is absolutely convergent, conditionally convergent, or divergent.

 ∑n=1∞n22n\sum_{n=1}^{\infty}\frac{n^2}{2^n}  

a)

Absolutely Convergent

b)

Conditionally Convergent

c)

Divergent

2.

Determine whether the series is absolutely convergent, conditionally convergent, or divergent.

 ∑n=1∞n2−1n2+1\sum_{n=1}^{\infty}\frac{n^2-1}{n^2+1}  

a)

Absolutely Convergent

b)

Conditionally Convergent

c)

Divergent

3.

Determine whether the series is absolutely convergent, conditionally convergent, or divergent.

 ∑n=1∞(−1)n−12nn4\sum_{n=1}^{\infty}\left(-1\right)^{n-1}\frac{2^n}{n^4}  

a)

Absolutely Convergent

b)

Conditionally Convergent

c)

Divergent

4.

Determine whether the series is absolutely convergent, conditionally convergent, or divergent.

 ∑n=1∞(−1)n+1n\sum_{n=1}^{\infty}\frac{\left(-1\right)^{n+1}}{\sqrt{n}}  

a)

Absolutely Convergent

b)

Conditionally Convergent

c)

Divergent

5.

Determine whether the series is absolutely convergent, conditionally convergent, or divergent.

 ∑n=1∞n2+1n3+1\sum_{n=1}^{\infty}\frac{n^2+1}{n^3+1}  

a)

Absolutely Convergent

b)

Conditionally Convergent

c)

Divergent

6.

What is the Radius of Convergence for;

 ∑n=0∞xnn\sum_{n=0}^{\infty}\frac{x^n}{\sqrt{n}} 


a)

 R=0R=0  

b)

 R=12R=\frac{1}{2}  

c)

 R=1R=1  

d)

 R=∞R=\infty  

7.

Which of the following is the first 3 terms for the Maclaurin Series of;

 f(x)=sin⁡(x)f\left(x\right)=\sin\left(x\right)  


a)

 1+x+x221+x+\frac{x^2}{2}  

b)

 1−x22!+x44!1-\frac{x^2}{2!}+\frac{x^4}{4!}  

c)

 x−x33!+x55!x-\frac{x^3}{3!}+\frac{x^5}{5!}  

d)

 1+x+x21+x+x^2  

8.

 f(x)=e2xf\left(x\right)=e^{2x}  

Which of the following is the first 3 terms of the Maclaurin Series for;

a)

 1+2x+4x21+2x+4x^2  

b)

 1+2x+2x21+2x+2x^2  

c)

 2x−4x33+4x5152x-\frac{4x^3}{3}+\frac{4x^5}{15}  

d)

 1−2x2+2x531-2x^2+\frac{2x^5}{3}  

9.

Write one (1) thing you really enjoyed about this school year.

4 lines
10.

Do you intend to continue learning about math in the future?

a)

Yes, absolutely. Regardless of my career path.

b)

Yes, my future plans will require it, but that's ok with me.

c)

Maybe, only if my future plans require it.

d)

No, I can't wait to be done with advanced math.