I'm going to answer this because it provides an opportunity to show a simple method for examining the behavior of the test function. First the syntax from the documentation:

So let's try:

NestWhileList[# + 1 &, 0, (Print[#, " ", #2]; True) &, 2, 5] 

0 1

1 2

2 3

3 4

{0, 1, 2, 3, 4, 5} 

This lets you easily see what is being passed to the text function at each step, and automatically aborts after five steps.

Here is another example. We end the loop when a certain ratio is exceeded:

NestWhileList[# + 1 &, 0, (Print["prev: ", #, " current: ", #2]; 1 - #/#2 > 0.15) &, 2] 

{0, 1, 2, 3, 4, 5, 6, 7} 

Hopefully this method and example will help you work these things out for yourself more easily.

I'm going to answer this because it provides an opportunity to show a simple method for examining the behavior of the test function. First the syntax from the documentation:

So let's try:

NestWhileList[# + 1 &, 0, (Print[#, " ", #2]; True) &, 2, 5] 

0 1

1 2

2 3

3 4

{0, 1, 2, 3, 4, 5} 

The function (Print[#, " ", #2]; True) & lets you easily see what is being passed to the test function at each step, and automatically aborts after five steps because of the last argument.

Here is another example. We end the loop when a certain ratio is exceeded:

NestWhileList[# + 1 &, 0, (Print["prev: ", #, " current: ", #2]; 1 - #/#2 > 0.15) &, 2] 

{0, 1, 2, 3, 4, 5, 6, 7} 

Hopefully this method and example will help you work these things out for yourself more easily.