Question

What is thermodynamic limit? ​

Answer 1

Answer:

The thermodynamic limit, or macroscopic limit, of a system in statistical mechanics is the limit for a large number N of particles where the volume is taken to grow in proportion with the number of particles. 

Answer 2

It can be seen as a mere definition. It is used for many calculations and it yields reasonable results. It reads

T.L.≡N→∞, V→∞, N/V<∞

That is, the assumption is that the final quantity remains bounded, which makes sense because it is the density n and one expects it to behave that way, even intuitively. In any case you can find a more profound explanation almost anywhere.