Is (2R,3S)-2,3-dichloropentane optically inactive?

Two confusing thing about (2⁠*R*,3⁠*S*)-2,3-dichloropentane:


1. The 2 stereocenters have opposite absolute configuration.
2. But there is no plane of symmetry.


So, is (2⁠*R*,3⁠*S*)-2,3-dichloropentane optically inactive? 


(This is actually a follow-up question of:
[Monochlorination of 2-chloropentane and possible enantiomer products](https://chemistry.stackexchange.com/questions/74261/monochlorination-of-2-chloropentane-and-possible-enantiomer-products?noredirect=1#comment130593_74261))




To have an optically inactive meso compound with two chiral centers:


1) the chiral centers must have opposite configuration


2) the chiral centers must have the same set of fragments bonded to them


Among other things the 2 carbon has a methyl group bonded to it versus the 3 carbon having an ethyl group instead. You do not satisfy (2), so you do not have the symmetry required for a meso compound, and the molecule is still chiral and optically active.


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