To describe the sequence
-
Identify the sequence:
- The first term
is - The second term
is - The third term
is
- The first term
-
Find a common pattern:
- The denominators of the fractions show a pattern:
is is is
However, for a better consistent arithmetic operation, let's express the fractions as decimals for easier examination.
- The denominators of the fractions show a pattern:
-
Observe the differences:
- The difference from the first to the second term is
- The difference from the second to the third term is
We notice that the denominator increases as
increases. - The difference from the first to the second term is
-
Setting a general formula:
- The denominators seem to relate to square terms or recursive elements.
- The fractions seem to converge towards a simpler formula while they increase steadily.
Let's express them using
:A potential formula for the
-th term can be expressed as:Therefore:
Hence, using this formula style, we write:
To conform to the requested format:
Thus the final answer in the specified format will be: