Ratio and Root Tests Quiz

Log In

---

1. Test $\sum_{n=1}^\infty \dfrac{(-1)^{n-1}}{3^n(n-1)!}$ for convergence.

   (a) Converges by the fundamental theorem of algebra
   (b) Converges by the ratio test
   (c) Diverges by the root test
   (d) Diverges by the test for divergence

---

2. Does $\sum_{n=1}^\infty (-1)^n \left(\dfrac{\ln{(n)}}{n}\right)^n$ converge absolutely, converge conditionally, or diverge?

   (a) Converges absolutely by the root test
   (b) Converges conditionally by the root test
   (c) Diverges by the ratio test
   (d) Diverges by the root test

---

3. Test $\sum_{n=1}^\infty \dfrac{2^n \cdot n!}{n^n}$ for convergence.

   (a) Diverges by the ratio test
   (b) Diverges by the root test
   (c) Converges by the integral test
   (d) Converges by the ratio test

---

4. Test $\sum_{n=1}^\infty \dfrac{2^n}{3^n \cdot 4n}$ for convergence.

   (a) Converges conditionally by the ratio test
   (b) Converges absolutely by the ratio test
   (c) Diverges by the ratio test
   (d) Diverges by the test for divergence

---

5. Test $\sum_{n=1}^\infty \dfrac{(n!)^2}{(2n)!}$ for convergence.

   (a) Diverges by the ratio test
   (b) Diverges by the root test
   (c) Converges by the ratio test
   (d) Converges by the factorial test

---

---

Infinite Series Main Page

---