Answer:
Diverges
Step-by-step explanation:
The given sequence is:
11, 22, 44, 88,.....
Now, [tex]a_{1}=11=2^0{\times}11[/tex],
[tex]a_{2}=22=2^1{\times}11[/tex],
[tex]a_{3}=44=2^2{\times}11[/tex],
[tex]a_{4}=88=2^3{\times}11[/tex]
Thus,the nth term will be: [tex]a_{n}=2^{n-1}{\times}11[/tex].
Now, as [tex]\lim_{n \to \infty} a_n[/tex], then
[tex]\lim_{n \to \infty} a_n=2^{n-1}{\times}11=+{\infty}[/tex]
Since, as [tex]n{\rightarrow}{\infty}[/tex], [tex]a_{n}{\rightarrow}+{\infty}[/tex], thus the given sequence diverges.
