Expectation example

#1

x = 2^(N+1)-2
how it will calculated
bcz my answer is not maching with this

#2

what is the value of n?

#3

n can be any value given by user but my question is how did it calculated mathematically
in the video lecture of probability expectation

#4

for more better understanding read about it and watch video again. And if n is very large it can be calculated using mod operation by a prime number. Thanks