Answer
True statement
Work Step by Step
We are given:
1) $\{a_n\}$ decreasing
2) $a_n>0$ for all $n$
$\{a_n\}$ is decreasing, which means the sequence is monotonic.
$a_n>0$ for all $n$ and $\{a_n\}$ decreasing, therefore $\{a_n\}$ is bounded below.
As $\{a_n\}$ is bounded and monotonic, which means $\{a_n\}$ is convergent.
So the statement is TRUE.