Infinite Series

Infinite Series

Let's Consider an example

 $\sum_{n=1}^{\infty}\frac{n}{n+1}$  

Open Ended

Does the series converge or diverge?

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

Open Ended

Does the series converge or diverge?

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

The Harmonic Series

•  $\sum_{n=1}^{\infty}\frac{1}{n}$  

• Let's look at some partial sums (SAGE/DESMOS)

• https://www.desmos.com/calculator/8op6xpfuks

Open Ended

 $\sum_{n=1}^{\infty}\frac{\left(-3\right)^{\left(n+1\right)}}{4^{\left(n-1\right)}}$  Does this converge or diverge? IF it converges can you find the limit?

Open Ended

 $\sum_{n=1}^{\infty}e^{2n}$  Does this converge or diverge? IF it converges can you find the limit?

Poll

Series? How do you feel about them?

• i hate this so much

• I'm confused

• way better than integration

• I have got this so far