Hello thereI can't understand how adding a capacitor reduces the signal gain to 1?
At DC the capacitor acts as an open connection. Therefore R1 is effectively taken out of the equation. The remaining circuit is very similar to a voltage follower configuration with R2 in its feedback path. A voltage follower as you probably know has a gain of 1.
And with no current through R1, then R2 also has no effect on the DC gain, so the circuit becomes a follower.The remaining circuit is very similar to a voltage follower configuration with R2 in its feedback path.