The sequence Three-halves, four-thirds, five-fourths, six-fifths, ellipsis, is a converging sequence, that converges to 1.
Hence, the 3rd option: "The sequence converges to 1.", is the best choice.
What does converging and diverging mean?
Converging signifies a movement toward something. Diverging denotes moving away from something.
How to solve the question?
In the question, we are given a sequence: Three-halves, four-thirds, five-fourths, six-fifths, ellipsis.
This can be shown as 3/2, 4/3, 5/4, ...
The general term of this series is (n + 2)/(n + 1).
As it is going on continuously to infinite,
The term can be shown as:
[tex]lim_{n\rightarrow \infty }\frac{n + 2}{n + 1} \\= lim_{n\rightarrow \infty }1 + \frac{1}{n+1} \\=lim_{n\rightarrow \infty }1 + lim_{n\rightarrow \infty }\frac{1}{n+1} \\= 1 + 0 \\= 1[/tex]
Thus, we can see that the sequence, gradually moves to a point. Thus it is converging in nature.
Also, the point it converges is 1.
Hence, 3rd option is the best choice.
Learn more about converging and diverging sequences at
https://brainly.com/question/21654304
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