Which expression(s) will be positive for all positive integers n

A. 2(to the nth power)-n
B. n-2(to the nth power)
C. (n+1)-2(to the nth power)
D. 2(to the nth power)- (n-1)
E. 2(to the nth power)+ n

A. Test for n=1
2^1 - 1 = 1
all n>1 will also yield positive results.

B. Test for n=1
1 - 2^1 = 0
technically, zero is not positive.

C. for n=1,
(1+1) - 2^1 = 0
zero is not positive

for n=2,
(2+1) - 2^2 = -1
negative

D. for n=1
2^1 - (1-1) = 2
positive

for n=2
2^2 - (2-1) = 3
positive

E. for n=1
2^1 + 1 = 3
positive and will be positive for all n>1

Answer: A, D, E