Question

Determine whether the sequence converges or diverges. If it converges, give the limit.

Answer 1

The sequence is a geometric sequence with a common ratio of 2. since the common ratio is greater than 1, the sequence diverges.

Answer 2

Answer:

Diverges

Step-by-step explanation:

The given sequence is:

11, 22, 44, 88,.....

Now, $a_{1}=11=2^0{\times}11$,

$a_{2}=22=2^1{\times}11$,

$a_{3}=44=2^2{\times}11$,

$a_{4}=88=2^3{\times}11$

Thus,the nth term will be: $a_{n}=2^{n-1}{\times}11$.

Now, as $\lim_{n \to \infty} a_n$, then

$\lim_{n \to \infty} a_n=2^{n-1}{\times}11=+{\infty}$

Since, as $n{\rightarrow}{\infty}$, $a_{n}{\rightarrow}+{\infty}$, thus the given sequence diverges.