Question

What will be the limit of the following sequence as n tends to infinity? Will the sequence converge or diverge?

`lim_(n rarr oo)a_n` where `a_n= (1+sinn)^(1/n)`

Answer 1

1

Explanation:

`lim_(n→∞)a_n=lim_(n→∞)(1+sinn)^(1/n)`
`=(1+sin∞)^(1/∞)`
`=(1+`(any number between -1 and 1)`)^0`
`=1`
this implies that given sequence convergent and it converges to 1