# maths

posted by .

prove that : 2^n + 2^n-1 / 2^n+1 - 2^n = 3/2

• maths -

( 2 ^ n + 2 ^ ( n - 1 ) ) / ( 2 ^ ( n + 1 ) - 2 ^ n ) Multiply both sides by ( 2 ^ ( n + 1 ) - 2 ^ n )

________________________________________

( 2 ^ n ) * 2 ^ ( n + 1 ) = 2 ^ ( 2 n + 1 )

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

2 ^ ( 2 n + 1 ) + 2 ^ 2 n = 3 * 4 ^ n

2 ^ ( 2 n ) * 2 ^ ( 2 n ) = ( 2 ^ ( 2 n ) ) ^ 2 = 2 ^ ( 4 n )

________________________________________

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

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

3 * 4 ^ n / ( 2 * 4 ^ n ) = 3 / 2

## Similar Questions

1. ### Maths

X and Y are points on the sides BC and AC of a triangle ABC respectively such that angle AXC = angle BYC and BX = XY. Prove that AX bisects the angle BAC. I believe the first step is to prove ABXY is a cyclic quadrilateral. Unfortunately, …
2. ### Advanced Maths (Vectors) AQA Level

Triangle ABC with D, E and F the midpoints of BC, AC, and AB. G is the midpoint of AD such that the ratio AG:GD =2:1, VECtors AB =p and BC =q Prove that B, G and E are collinear. prove the same results for point C, G and G
3. ### Advanced Maths (Vectors) AQA Level

Triangle ABC with D, E and F the midpoints of BC, AC, and AB. G is the midpoint of AD such that the ratio AG:GD =2:1, VECtors AB =p and BC =q Prove that B, G and E are collinear. prove the same results for point C, G and F
4. ### maths

prove that 2 2 2 2 (n-1) + n + (n+1) = 3n +2
5. ### maths

If a+b+c=0 then prove that a^4+b^4+c^4=2(a^2b^2+b^2c^2+c^2a^2)
6. ### maths

prove that: 1/1+x^b-a + x^c-a + 1/1+x^a-b +x^a-c = 1
7. ### maths

If the sum of the squares of the roots of the quadratic equation ax^2 + bx + c = 0 is m:n, prove that b^2= 2ac + 4a^2 I really have no idea how to prove it so pls help
8. ### DISCRETE MATHS

Prove that for every set S, Ø \subseteq( S. i need to Use vacuous proof. i know that vacuous proof is when the hypothesis is always False. but for this i find it very difficult please can you help me prove this?
9. ### Maths

prove that 2+2=5
10. ### Maths

Prove that 0! = 1

More Similar Questions