Answer
No (example: the harmonic series)
Work Step by Step
If the terms of a series with positive terms decrease to zero, it doesn't necessarily mean that the series converges. An example proving this is the harmonic series:
$\sum_{k=1}^{\infty} \dfrac{1}{k}=1+\dfrac{1}{2}+\dfrac{1}{3}+......$
The terms $\dfrac{1}{k}$ are positive and decrease to zero, but the series doesn't converge.
