The Nth Term Test for Divergence Worksheet with Answer Key

What's on the worksheet

1. Find the limit of the terms, if it exists, and say what the nth term test concludes.
   \sum_{n=1}^{\infty} \dfrac{4n^3 - n}{7 - 2n^3}\sum_{n=3}^{\infty} \left(\dfrac{n+1}{n-2}\right)^n\sum_{n=2}^{\infty} \dfrac{\sqrt{n}}{\ln n}\sum_{n=1}^{\infty} \dfrac{3^n + n^5}{n^4 + 2 \cdot 3^n}\sum_{n=1}^{\infty} \dfrac{(\ln n)^3}{n}
2. Find _n ∞ a_n for the series below, and state what the nth term test concludes about it, including where its partial sums go.
3. Consider the series below.
4. Noah settles three series.
5. Suppose _n=1^∞ a_n converges.
6. Chloe writes: