I solved the above exercise. And the exercise below is based on the exercise above.
Here, I managed to show the first equality of (i). But I can't find a way how to prove the second equality of (i) at all. Also, I tried to solve (ii) first by using Stirling formula. But, the calculations only get complicated and I can't get the required result. Now I am totally stuck.. Could anyone please help me how to solve this exercise 2? or at least give me some hints?