Problem: In the sequence .
(1) the sum increases without limit.
(2) the sum decreases without limit.
(3) the difference between any term of the sequence and zero can be made less than any positive quantity no matter how small.
(4) The difference between the sum and can be made less than any positive quantity no matter how small.
(5) the sum approaches a limit.
Answer Choices:
A. only (3) and (4) are correct statements
B. only (5) is a correct statement
C. only (2) and (4) are correct statements
D. only (2), (3) and (4) are correct statements
E. statements (a), (b), (c) and (d) are all incorrect.
Solution:
This sequence is an infinite geometric progression with . Thus if is its first term and its sum, we have
Hence (4) and (5) are correct statements.