This is what I want to analyze because I see it used in some 'typical application' circuit in datasheets:

Here is a Link to Falstad simulation. I would expect the capacitor to be worse then useless in the simulation, because (1) the AC-source is ideal and (2) it may act as a low- or highpass filter depending on the R and C size.
Next I will simulate in LTSpice. V2 is 10 mV @ 50 Hz. Using the step commando, the simulation will substitute {X} (the capacitor value) for the listed values and simulate for each step.


Now it's time to test this in real life. With one minor change: I will increase V2 to 1 V because 10 mV is hard to see clearly on my oscilloscope because of (I assume) ambient noise. The simulation chart looks the same except the sine wave is 1.5-3.5 V.
Here are the test results:
| Capacitor | Vout (min) | Vout (max) | | ------------ | ---------- | ---------- | | 102 (1 nF) | 2.40 | 2.48 | | 103 (10 nF) | 2.32 | 2.52 | | 104 (100 nF) | 2.00 | 2.88 | | 105 (1 uF) | 1.92 | 2.96 | | 106 (10 uF) | 1.92 | 2.96 |
From some additional simulations I find out the minimum value for C1 to prevent attenuation would be about 470 nF.
When I remove V1, R1 and R2 competely then even a 1 nF capacitor shows no attenuation whatsoever and any DC offset on the input signal is completely removed.
What is the purpose of R1/R2?