Infinite Series and Partial Sums Worksheet with Answer Key

What's on the worksheet

1. A series _n=1^∞ a_n has partial sums S_n = \frac{3n}{3n + 5}
2. Find a formula for S_n and the sum of the series, or show that the series diverges.
   \displaystyle\sum_{n=1}^{\infty} \dfrac{2n+1}{n^2(n+1)^2}\displaystyle\sum_{n=1}^{\infty} \dfrac{1}{\sqrt{n} + \sqrt{n+1}}
3. Decide whether each series converges.
4. Let a_n = 1n(n+1)(n+2).
6. Let T be the sum T = \frac{1}{43} + \frac{1}{44} + \cdots + \frac{1}{210}