Question

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

11, 22, 44, 88, ...

Answer 1

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.

Answer 2

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