Question 1

Determine whether the series $\sum\limits_{n=1}^{\infty} \frac{1}{n^{1.1}}$ converges or diverges.

Accepted Answer

B) Converges

Question 2

Does the series $\sum\limits_{n=1}^{\infty} n^2 e^{-n}$ converge or diverge?

Accepted Answer

A) Converges

Question 3

Determine the convergence of the series $\sum\limits_{n=1}^{\infty} \frac{2n+3}{\sqrt{5n^2+2n+6}}$.

Accepted Answer

A) Diverges

Question 4

Find the sum of the series $\sum\limits_{n=1}^{\infty} \frac{1}{n(n+3)}$.

Accepted Answer

C) Converges

Question 5

Does the series $\sum\limits_{n=1}^{\infty} \left( \sqrt{n+1} - \sqrt{n} \right)$ converge or diverge?

Accepted Answer

B) Diverges

Question 6

Find the sum of the series $\sum\limits_{n=1}^{\infty} \frac{3}{2^n}$.

Accepted Answer

D) $3$

Question 7

Evaluate the sum $\sum\limits_{n=1}^{\infty} \frac{(-1)^{n+1}}{6^n}$.

Accepted Answer

D) $\frac{1}{7}$

Question 8

Determine whether the series $\sum\limits_{n=1}^{\infty} \frac{1}{n^2+1}$ converges or diverges.

Accepted Answer

B) Converges

Question 9

Does the series $\sum\limits_{n=1}^{\infty} \frac{1}{n^2+2}$ converge or diverge?

Accepted Answer

B) Converges

Question 10

Use the integral test to determine whether the series $\sum\limits_{n=2}^{\infty} \frac{1}{n (\ln n)^2}$ converges or diverges.

Accepted Answer

A) Converges

Question 11

Use the limit comparison test to determine if $\sum\limits_{n=1}^{\infty} \frac{7n+6 \sin n}{n^2+7}$ converges or diverges.

Accepted Answer

B) Converges

Question 12

Use the ratio test to determine if the series $\sum\limits_{n=1}^{\infty} \frac{2^n}{n!}$ converges or diverges.

Accepted Answer

A) Converges

Question 13

Use the root test to determine if the series $\sum\limits_{n=1}^{\infty} \frac{(\ln n)^n}{n^n}$ converges or diverges.

Accepted Answer

A) Diverges

Question 14

Does the series $\sum\limits_{n=1}^{\infty} \frac{5^n}{n^2}$ converge or diverge?

Accepted Answer

A) Diverges

Question 15

Determine the convergence of the series $\sum\limits_{n=1}^{\infty} \frac{3n}{n^2+7}$.

Accepted Answer

A) Converges

Question 16

A medical researcher models the decay of a drug in the bloodstream using the series $\sum\limits_{n=1}^{\infty} \frac{1}{2^n}$. What is the total amount of drug present after infinite time?

Accepted Answer

A) 1

Question 17

A financial analyst uses the series $\sum\limits_{n=1}^{\infty} \frac{1}{n^3}$ to model diminishing returns. Does the series converge or diverge?

Accepted Answer

A) Converges

Question 18

A chemist analyzes a reaction rate modeled by $\sum\limits_{n=1}^{\infty} \frac{n}{2^n}$. What is the sum of the series?

Accepted Answer

A) 2

Question 19

A historian models population growth using $\sum\limits_{n=1}^{\infty} \frac{1}{n}$, the harmonic series. Does this series converge or diverge?

Accepted Answer

A) Diverges

Convergence and Divergence of Series: Techniques and Applications

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