# Is every finitely generated group colimit of residually finite groups

I was listening to a talk about ultraproducts and one result there suggested, that every finitely generated group can be written as a colimit of residually finite groups (over a directed system). As I don't see a trivial proof, I expect it to be false (it is a statement about all groups). But I don't see a counterexample.

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$$H:= \langle a,b,c,d \mid ba = a^2b, cb=b^2c, dc=c^2d, ad=d^2a \rangle.$$