Practice: Ratio Test

4 Activities

Determine whether the series ∑n=1∞1n!{\displaystyle \sum_{n=1}^\infty}\frac{1}{n!}n=1∑∞​n!1​ converges or diverges.

It converges

It diverges

Cannot be determined

I don't know

Determine whether the series ∑n=1∞1n!{\displaystyle \sum_{n=1}^\infty}\frac{1}{n!}n=1∑∞​n!1​ converges or diverges.

Practice Question
Determine whether ∑n=1∞(n2)!nn\sum\limits^\infty_{n=1}\frac{(n^2)!}{n^n}n=1∑∞​nn(n2)!​ converges or diverges.

Practice: Ratio Test
Determine whether the series ∑n=1∞1n!{\displaystyle \sum_{n=1}^\infty}\frac{1}{n!}n=1∑∞​n!1​ converges or diverges.

Practice: Ratio Test
Determine whether the series ∑n=1∞1n!{\displaystyle \sum_{n=1}^\infty}\frac{1}{n!}n=1∑∞​n!1​ converges or diverges.

Practice Question
Determine whether ∑n=1∞(n2)!nn\sum\limits^\infty_{n=1}\frac{(n^2)!}{n^n}n=1∑∞​nn(n2)!​ converges or diverges.

Practice Question
Determine whether ∑n=1∞(n2)!nn\sum\limits^\infty_{n=1}\frac{(n^2)!}{n^n}n=1∑∞​nn(n2)!​ converges or diverges.

Practice: Ratio Test
Determine whether the series ∑n=1∞1n!{\displaystyle \sum_{n=1}^\infty}\frac{1}{n!}n=1∑∞​n!1​ converges or diverges.