Answer
NO
Work Step by Step
As we can see that $(\dfrac{1}{2})\Sigma_{n=1}^\infty a_n$ is a convergent series of positive numbers.
Thus, $(2)\Sigma_{n=1}^\infty a_n= \Sigma_{n=1}^\infty 2a_n$ also diverges for $2a_n \geq a_n$
Therefore, we will not get the largest convergent series of positive numbers.
Thus, the correct answer is No.
