Hello,

When you have a system that samples the output every T seconds, we say the maximum bandwidth that can be measured is f=1/2T (nyquist).

My question is what is the bandwidth that should be used to calculate the contribution of the thermal noise on the output value?

Is the equation sqrt(4KTR*1/T) or sqrt(4KTR*1/2T)

Thank you

 

Neither.
The thermal noise will be aliased by the sampling, so the noise bandwidth is determined by the usual anti-alias filter at the sampling circuit input.
If you don't understand aliasing, look up references on sample-data systems.