You just have to properly define what you mean by "imperceptible" and you are good to go. Now you can look for a bounded approximation. See how it changes as things get bigger. See if it can be improved.

Bounds and approximation are generally a very useful tool. Properties simplifications and working on sub parts can also yield interesting results.

Generally I would say that if you can’t prove something, trying something close but simpler is nearly always a good idea.