Telescoping series practice problems
Telescoping series: split the term, watch the middle cancel, and take the limit of the partial sums. 10 problems with worked solutions; in 10 of them every equation is proved by a computer algebra system.
Find the sum of \( \displaystyle \sum_{n=1}^{\infty} \frac{2}{n^{2} + 7 n + 12} \), or show that it diverges.
Find the sum of \( \displaystyle \sum_{n=1}^{\infty} \frac{6}{n^{2} + 5 n + 4} \), or show that it diverges.
Find the sum of \( \displaystyle \sum_{n=1}^{\infty} \frac{5}{n^{2} + 4 n + 3} \), or show that it diverges.
Find the sum of \( \displaystyle \sum_{n=1}^{\infty} \frac{2}{n^{2} + 6 n + 8} \), or show that it diverges.
Find the sum of \( \displaystyle \sum_{n=1}^{\infty} \frac{1}{n^{2} + 5 n + 6} \), or show that it diverges.
Find the sum of \( \displaystyle \sum_{n=1}^{\infty} - \frac{1}{\sqrt{n + 1}} + \frac{1}{\sqrt{n}} \), or show that it diverges.
Find the sum of \( \displaystyle \sum_{n=1}^{\infty} \frac{6}{n^{2} + 8 n + 15} \), or show that it diverges.
Find the sum of \( \displaystyle \sum_{n=1}^{\infty} \frac{4}{n^{2} + 3 n} \), or show that it diverges.
Find the sum of \( \displaystyle \sum_{n=1}^{\infty} \frac{6}{n^{2} + 4 n + 3} \), or show that it diverges.
Find the sum of \( \displaystyle \sum_{n=1}^{\infty} \frac{2}{n^{2} + 2 n} \), or show that it diverges.