The value of 2^n + 2^(n-1) / 2^(n+1) - 2^n is

2^n + 2^n-1 / 2^n+1 - 2^n

2^n ( 1+ 0.5) / 2^n ( 2 - 1)

= 3/2

take 2^n common from numerator and denominator and cancel each other...which leaves
2^n(1+ 2^-1) /
2^n(2^1 - 1)
=3/2

Taking various values of n we get answer as 3/2
like n=2
4+2/8-4=3/2

by putting the value of n we get answer
n=1 then value of equation is 3/2
n=2 then value also 3/2
option 4

take 2^n outside and cancel it.

= [ 2^n( 1 + 1/2 ) ] / [ 2^n ( 2 - 1 ) ]
= (3/2)/1
= 3/2
option 4.

[2^n(1+1÷2)]÷[2^n(2-1)]=3÷2,so option 4 is the answer

a^mn=a^m+a^n
2^n+2^n/2 / 2(2^n)-2^n
2(2^n)+2^n/2 * 1/(2(2^n)-2^n)
2^n(3)/2 * 1/2^n(1)
3/2

2^n + 2^(n-1) / 2^(n+1) - 2^n
=[{(2*2^n) + 2^n}/2] / 2^n
={(3*2^n)/2} / 2^n
=3*2^n / 2*2^n
=3/2

2^n+2^(n-1)/n^(n+1)-2^n = (2^n+(2^n/2))/(2^n*2-2^n)
=2^n(1+1/2)/2^n(2-1)
=1+1/2
=3/2

2^n + 2^(n-1) / 2^(n+1) - 2^n
=(2^n *2 +2^n) / (2^n*2*2 -2*2^n)
=2^n * (2+1) / 2^n *2 *(2-1)
=3/2

for Dividend of the fraction we've
2^n + 2^(n - 1) = 2^n + 2^n *2^-1 = 2^n(1+1/2)
simlly, for the Divisor of the fraction we've
2^(n + 1) - 2^n = 2^n * 2^1 - 2^n = 2^n (2 - 1)
hence, the fraction becomes
= 2^n(1 + 1/2)/2^n(2 - 1)
= (1+1/2)/(2 - 1)
= (3/2)/1
= 3/2
Option 4 is the correct answer.
therefore, the value 2^n + 2^(n-1) / 2^(n+1) - 2^n is 3/2

2^n+2^(n-1)/2^(n+1)-2^n

=2^n+(2^n/2)/2*2^n-2^n

={2^n(1+1/2)}/{2^n(2-1)}

=(1+1/2)/(2-1)

=3/2

2^n + 2^n-1 /2^n+1 - 2^n;
2^n(1 + 1/2)/ 2^n(2 - 1);
3/2.

2^n=y

y+y/2=3y/2

2y-y=y

3y/2y =3/2


therefore answer is 3/2
when we substitute y=3/2

2^3/2+2^3/2-1/(2^3/2+1-2^3/2

=2^3/2+2^1/2/(2^5/2-2^3/2)


= 2^1/2(2+1)/2^3/2(2-1)

= 3/2

2^n+2^n-1/2^n+1-2^n
=2^n (1+1/2)/2^n (2-1)
=2+1/2
=3/2

2^n+2^n-1/2n+1-2^n
= 2^ n ( 1 + 1 / 2 )/ 2^ n ( 2-1 ),
=2+ 1/2,
=3/2/1,
=3/2.

Given :
[ 2^n + 2^(n-1) ]/ [ 2^(n+1) -2^n]

= (2^n [ 1+0.5]) /(2^n [2-1])
=(1+0.5)/(2-1)
=1.5/1
=3/2

take any integer value say n=5 which gives the value of expression as 3/2.
now for evaluating the general term of answer..go through the following logic...
since the numerical answer is 3/2 , numerator must be greater than the denominator in the general term too...as u can see....(besides option 4) only option 3 is having greater numerator while the other have not...so we need to check only option 3....now put any arbitary integer/natural no. say n=2 which gives 2^3/2^1 = 4 which doesn't equal to 3/2...
so 3/2 is the only option which is correct for any case...u can affirm it by putting some more values of n...