Comparison Tests Quiz

Log In

---

1. Does $\sum_{n=1}^\infty \dfrac{n}{\sqrt{n^7 + 3}}$ converge or diverge?

   (a) Convergent since $\lim_{n \to \infty} \dfrac{n^{7/2}}{\sqrt{n^7 + 3}} = 5/2$
   (b) Convergent since $\lim_{n \to \infty} \dfrac{n^{7/2}}{\sqrt{n^7 + 3}} = 1$
   (c) Divergent since $\lim_{n \to \infty} \dfrac{n^{7/2}}{\sqrt{n^7 + 3}} = \infty$
   (d) Divergent since $\lim_{n \to \infty} \dfrac{n^{7/2}}{\sqrt{n^7 + 3}} = 1$

---

2. Does $\sum_{n=1}^\infty \dfrac{n+7}{n^2}$ converge?

   (a) Diverges since $\dfrac{n+7}{n^2} > \dfrac{1}{n^2}$
   (b) Diverges since $\dfrac{n+7}{n^2} > \dfrac{1}{n}$
   (c) Converges since $\dfrac{n+7}{n^2} < \dfrac{1}{n^2}$
   (d) Converges since $\dfrac{n+7}{n^2} < \dfrac{1}{n}$

---

3. Does $\sum_{n=1}^\infty \dfrac{1}{n!}$ converge?

   (a) Convergent by comparison with $\sum \dfrac{1}{2^n}$
   (b) Convergent by limit comparison with $\sum \dfrac{1}{n^2}$
   (c) Divergent by comparison with $\sum \dfrac{1}{2^n}$
   (d) Divergent by comparison with $\sum \dfrac{1}{n}$

---

4. Does $\sum_{n=1}^\infty \dfrac{e}{\sqrt{n} + \pi}$ converge?

   (a) Divergent since $\lim_{n \to \infty} \dfrac{e\sqrt{n}}{\sqrt{n} + \pi} = e$
   (b) Divergent since $\lim_{n \to \infty} \dfrac{e\sqrt{n}}{\sqrt{n} + \pi} = 1/e$
   (c) Convergent since $\lim_{n \to \infty} \dfrac{e\sqrt{n}}{\sqrt{n} + \pi} = e$
   (d) Convergent since $\lim_{n \to \infty} \dfrac{e\sqrt{n}}{\sqrt{n} + \pi} = 1/e$

---

5. Does $\sum_{n=1}^\infty \dfrac{1}{n5^n}$ converge or diverge?

   (a) Diverges by comparison to $\sum \dfrac{1}{5^n}$
   (b) Diverges by comparison to $\sum \dfrac{1}{10^n}$
   (c) Converges by comparison to $\sum \dfrac{1}{10^n}$
   (d) Converges by comparison to $\sum \dfrac{1}{5^n}$

---

---

Infinite Series Main Page

---