BC Calculus - Series Assessment

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

 $\sum_{n=1}^{\infty}\frac{n^2}{2^n}$  

• Absolutely Convergent

• Conditionally Convergent

• Divergent

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

 $\sum_{n=1}^{\infty}\frac{n^2-1}{n^2+1}$  

• Absolutely Convergent

• Conditionally Convergent

• Divergent

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

 $\sum_{n=1}^{\infty}\left(-1\right)^{n-1}\frac{2^n}{n^4}$  

• Absolutely Convergent

• Conditionally Convergent

• Divergent

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

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

• Absolutely Convergent

• Conditionally Convergent

• Divergent

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

 $\sum_{n=1}^{\infty}\frac{n^2+1}{n^3+1}$  

• Absolutely Convergent

• Conditionally Convergent

• Divergent

What is the Radius of Convergence for;

 $\sum_{n=0}^{\infty}\frac{x^n}{\sqrt{n}}$ 

•  $R=0$  

•  $R=\frac{1}{2}$  

•  $R=1$  

•  $R=\infty$  

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

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

•  $1+x+\frac{x^2}{2}$  

•  $1-\frac{x^2}{2!}+\frac{x^4}{4!}$  

•  $x-\frac{x^3}{3!}+\frac{x^5}{5!}$  

•  $1+x+x^2$  

 $f\left(x\right)=e^{2x}$  

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

•  $1+2x+4x^2$  

•  $1+2x+2x^2$  

•  $2x-\frac{4x^3}{3}+\frac{4x^5}{15}$  

•  $1-2x^2+\frac{2x^5}{3}$  

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

Evaluate responses using AI:

OFF

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

• Yes, absolutely. Regardless of my career path.

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

• Maybe, only if my future plans require it.

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