Alternating Series Quiz

Log In

---

1. Test $\sum_{n=1}^\infty \dfrac{(-1)^n\ln{\left(n+6\right)}}{n^2}$ for convergence.

   (a) Convergent since it is absolutely convergent by comparison to $\sum \dfrac{1}{n^{3/2}}$
   (b) Convergent (but not absolutely convergent by limit comparison to $\sum \frac{1}{n}$)
   (c) Divergent by the test for divergence
   (d) Convergent by the Monotone Convergence Theorem

---

2. Does $\sum_{n=1}^\infty \dfrac{(-1)^{n-1}n}{e^n}$ converge or diverge?

   (a) Convergent telescoping series
   (b) Convergent since $\dfrac{n}{e^n}$ decreases to $0$
   (c) Divergent by the test for divergence
   (d) Divergent telescoping series

---

3. Does $\sum_{n=1}^\infty (-1)^n \cos{(\pi/n)}$ converge or diverge?

   (a) Divergent by the test for divergence
   (b) Convergent by the comparison test
   (c) Convergent by the limit comparison test
   (d) Convergent by the integral test

---

4. Does $\sum_{n=1}^\infty (-1)^n\dfrac{\sqrt{n}}{n+3}$ converge?

   (a) Divergent by the test for divergence
   (b) Divergent telescoping series
   (c) Convergent since it is absolutely convergent
   (d) Convergent since $\dfrac{\sqrt{n}}{n+3}$ decreases to $0$

---

5. Does $\sum_{n=1}^\infty \dfrac{(-1)^n\cos{\left(n\right)}}{n^2}$ converge?

   (a) Divergent telescoping sum
   (b) Divergent by the test for divergence
   (c) Conditionally convergent
   (d) Absolutely convergent

---

---

Infinite Series Main Page

---