Which of the following sequences are unbounded?

Options

A. `(1+(1)/(n))^(n)`
B. `((2n+1)/(n+2))`
C. `(1+(1)/(n))^(n^(2))`
D. `tan n`

Answer

C, D

Explanation

(c ) `:.a_(n) =(1+(1)/(n))^(n^(2))`
For `n=1,a_(1)=2`,
for `n=2,a_(2)=(1+(1)/(2))^(4)=((3)/(2))^(4)=(3^(4))/(2^(4))=(81)/(16)=5.06" " [" approximate "]`
`lim_(nto oo)(1+(1)/(n))^(n^(2))=e^(lim_(nto oo)(1)/(n)xx^(n^(2)))=e^(lim_(nto oo)n)=e^(oo)=oo`
`:.{a_(n)}` represents unbounded sequence.
(b) `:.a_(n)=tann`
`a_(n)=n+(n^(3))/(3)+(2)/(15)n^(5)+"...."+oo`
and we know that `-oolttan nltoo`
So, `{a_(n)}` is unbounded sequence.