Answer:
The sequence converges to 1
Step-by-step explanation:
Given
[tex]\frac{2}{4}. \frac{3}{5}, \frac{4}{6}, \frac{5}{7},...[/tex]
Require
Description of the sequence
The given sequence follows:
[tex]\frac{2}{4}. \frac{3}{5}, \frac{4}{6}, \frac{5}{7},... \frac{n+1}{n+3}[/tex]
i.e.
[tex]T_n = \frac{n+1}{n+3}[/tex]
For every term,
[tex]\frac{n+1}{n+3} < 1[/tex]
In other words,
as the value of n increases, [tex]\frac{n+1}{n+3}[/tex] approaches 1
Hence, (c) is true
