Comparison and limit comparison tests practice problems
Compare with a p-series: the limit comparison test decides most rational and algebraic terms. 10 problems with worked solutions; in 10 of them every equation is proved by a computer algebra system.
Determine whether \( \displaystyle \sum_{n=1}^{\infty} \frac{4 n^{2} + 4 n + 4}{3 n^{4} + 4 n^{3} + 3 n^{2} + 2 n + 1} \) converges or diverges.
Determine whether \( \displaystyle \sum_{n=1}^{\infty} \frac{n + 1}{\sqrt{3 n^{5} + n^{4} + 3 n^{3} + 2 n^{2} + n + 3}} \) converges or diverges.
Determine whether \( \displaystyle \sum_{n=1}^{\infty} \frac{3 n^{2} + 4 n + 2}{n^{4} + 3 n^{3} + 4 n^{2} + 3 n + 3} \) converges or diverges.
Determine whether \( \displaystyle \sum_{n=1}^{\infty} \frac{3}{4 n + 2} \) converges or diverges.
Determine whether \( \displaystyle \sum_{n=1}^{\infty} \frac{n + 2}{2 n^{3} + 2 n^{2} + 4 n + 1} \) converges or diverges.
Determine whether \( \displaystyle \sum_{n=1}^{\infty} \frac{n^{2} + n + 4}{\sqrt{3 n^{5} + 3 n^{4} + 2 n^{3} + 3 n^{2} + 2 n + 1}} \) converges or diverges.
Determine whether \( \displaystyle \sum_{n=1}^{\infty} \frac{2 n + 2}{4 n^{2} + 4 n + 2} \) converges or diverges.
Determine whether \( \displaystyle \sum_{n=1}^{\infty} \frac{n^{2} + 4 n + 3}{3 n^{4} + n^{3} + 3 n^{2} + 2 n + 4} \) converges or diverges.
Determine whether \( \displaystyle \sum_{n=1}^{\infty} \frac{4 n + 1}{\sqrt{2 n^{5} + 3 n^{4} + 2 n^{3} + 3 n^{2} + n + 1}} \) converges or diverges.
Determine whether \( \displaystyle \sum_{n=1}^{\infty} \frac{4 n + 1}{\sqrt{2 n^{5} + 3 n^{4} + 3 n^{3} + 3 n^{2} + 2 n + 2}} \) converges or diverges.