An Exercise on Sum to Infinity | Convergence & Applications

Question 1 MC
Find the sum to infinity of \( 9 + 3 + 1 + \frac{1}{3} + \cdots \).
A. \( 12 \)     B. \( 13.5 \)     C. \( 15 \)     D. \( 18 \)

Question 2 MC
Which series does not converge?
A. \( 4 + 2 + 1 + 0.5 + \cdots \)     B. \( 1 - \frac{1}{2} + \frac{1}{4} - \frac{1}{8} + \cdots \)
C. \( 10 + 5 + 2.5 + 1.25 + \cdots \)     D. \( 2 + 6 + 18 + 54 + \cdots \)

Question 3 Short Answer
Convert \( 0.\overline{45} \) to a fraction.

Question 4 Short Answer
Find the sum to infinity of \( 27 + 9 + 3 + 1 + \cdots \).

Question 5 MC
A ball rebounds to \( \frac{2}{3} \) of its previous height. If dropped from 81 m, total distance traveled is:
A. \( 243 \) m     B. \( 405 \) m     C. \( 324 \) m     D. \( 486 \) m

Question 6 Short Answer
Express \( 1.\overline{6} \) as a fraction.

Question 7 MC
The sum to infinity of a GP is 24 and the first term is 12. Find the common ratio.
A. \( \frac{1}{2} \)     B. \( \frac{1}{3} \)     C. \( \frac{2}{3} \)     D. \( \frac{3}{4} \)

Question 8 Short Answer
A person walks 40 m east, then 20 m west, then 10 m east, and so on. Find the total distance traveled.

Question 9 Short Answer
The sum to infinity of a GP is twice its first term. Find the common ratio.

Question 10 Short Answer
Write \( 0.\overline{27} \) as a fraction and verify by long division.