Tutorial Week 12
Alternating Series
Q1: Does the series \(\sum_{n=1}^\infty \frac{(-1)^nn^2}{n^2+n}\) converge? If it converges, is it absolutely or conditionally convergent?
Q2: Does the series \(\sum_{n=1}^\infty \frac{(-1)^nn}{n^2+n}\) converge? If it converges, is it absolutely or conditionally convergent?
Ratio Test
Q3: Use the ratio test to test the convergence of \(\sum_{n=1}^\infty \frac{(-5)^n}{(n!)^2}\).
Q4: Use the root test to test the convergence of \(\sum_{n=1}^\infty (\frac{4 + n + ln(n)}{n^2})^n\).
