How to do amortized analysis for an expanding array?
This looks like a homework problem, so I will try to highlight the skeleton of the proof. 


The cost of inserting and taking an element out of an array is 1
The cost of resizing an array is equal to the number of elements moved to the new/bigger array. 
As a simple case, consider you increase the size of array by 1. Calculate the total cost of resizing? 


Repeat the above analysis by doubling the size of array and check which one is better i.e. doubling the size OR increasing by 1? Calculate the amortized cost for both cases? Then you should be good to answer your own question...