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Series & convergence quiz
Five questions on Series & convergence. Answer all 5 to see your score.
Question 1 of 5
Let a_n = \frac{3n^2 + 2n}{5n^2 - 1} for n \ge 1. What is \lim_{n \to \infty} a_n?
Question 2 of 5
Use the integral test on \sum_{n=2}^{\infty} \frac{1}{n \ln n}. What does it show?
Question 3 of 5
Determine the behavior of \sum_{n=1}^{\infty} \frac{\sqrt{n}}{n^2 + 1}.
Question 4 of 5
Classify the series \sum_{n=1}^{\infty} (-1)^n \frac{n}{n^2 + 1}.
Question 5 of 5
The power series \sum_{n=0}^{\infty} \frac{(-1)^n x^{2n}}{(2n)!} is the Taylor series at 0 of a familiar function. What is its radius of convergence?