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Your opamp circuit can amplify DC. The input current of the opamp causes a DC voltage at the (-) input that should be cancelled with the same voltage at the (+) input created by the resistor to ground.
The (-) input has a voltage caused by the input current in the feedback resistors and the opamp amplifies this voltage. Then the offset voltage at the output causes non-symmetrical clipping when the signal level is high.
In a brief, the resistor is only useful for OPs with bipolar transistor input stage that don't utilize input current compensation. It's degrading performance of MOS or JFET OPs (increasing noise) and also of input current compensated amplifiers (Ios has the same order of magnitude as Ib, any additional input resistor typically increases overall offset and offset drift).
In other words, it's a typical element of OP circuit designed in the sixties and seventies. People are copying it from text book circuits without understanding why.
@Fvm: It means that the new OP wouldn't need it as the new ones don't use BJT's. I would like to make the physical circuit in order to know the offset effect it can cause on new OpAmps.
If the OP input current is negligible, R3 neither compensates nor causes offset voltage. It adds however resistor noise and makes the non-inverting input susceptible to capacitively coupled interfering signals. In so far I prefer your initial choice to ground the input directly.
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