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nobillionaireNobley

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

boffeemadrid

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.

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