From the following statements, select all that are true.

None of the other statements is true.

If every proper subsequence of a sequence left curly bracket a subscript n right curly bracket converges, then left curly bracket a subscript n right curly bracket converges as well.

There is a convergent sequence left curly bracket a subscript n right curly bracket with a subscript n not equal to $0$ for each n element of straight natural numbers such that left curly bracket $1$ divided by a subscript n right curly bracket diverges.

There is a sequence that contains, for each number n element of straight natural numbers, a subsequence with limit $1$ over n$.$