2 Answers

Assad Ullah · Answer 1 · 2017-01-29T02:15:31+0000

Answer:

Diverges

Explanation:

The given sequence is:

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

Now,
$a_(1)=11=2^0{*}11$ ,

$a_(2)=22=2^1{*}11$ ,

$a_(3)=44=2^2{*}11$ ,

$a_(4)=88=2^3{*}11$

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

Now, as
$\lim_(n \to \infty) a_n$ , then

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

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

Raghumudem · Answer 2 · 2017-02-01T22:34:53+0000

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

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