1.8 Infinite geometric series Quiz

1. Which series has a sum to infinity?

• A. $1 + 2 + 4 + \cdots$
• B. $5 - 5 + 5 - \cdots$
• C. $8 - 4 + 2 - \cdots$
• D. $1 + 1.1 + 1.21 + \cdots$

2. Find the sum to infinity of $12 + 4 + \frac43 + \cdots$.

• A. $16$
• B. $18$
• C. $36$
• D. $9$

3. A geometric series has $S_\infty = 20$ and $r = 0.75$. Find $u_1$.

• A. $15$
• B. $26.7$
• C. $5$
• D. $80$

4. For which values of $x$ does $1 + \frac{x}{2} + \frac{x^2}{4} + \cdots$ converge?

• A. $|x|<2$
• B. $|x|<\frac12$
• C. $x<2$
• D. $|x|<1$

5. Write $0.\dot{3}\dot{6}$ ($0.363636\ldots$) as a fraction.

• A. $\frac{36}{100}$
• B. $\frac{4}{11}$
• C. $\frac{9}{25}$
• D. $\frac{36}{90}$