Home » Mathematics » Simplify (frac{3(2^{n+1}) – 4(2^{n-1})}{2^{n+1} – 2^n})

Simplify (frac{3(2^{n+1}) – 4(2^{n-1})}{2^{n+1} – 2^n})

Simplify (frac{3(2^{n+1}) – 4(2^{n-1})}{2^{n+1} – 2^n})

  • A.
    2n+1
  • B.
    2n-1
  • C.
    4
  • D.
    1/4
Correct Answer: Option C
Explanation

Start by expanding (frac{3(2^{n+1}) – 4(2^{n-1})}{2^{n+1} – 2^n}):

(frac{3 times 2^n times 2^1 – 2^2 times 2^n times 2^{-1}}{2^n times 2 – 2^n})

Solving the equation above gives;

(frac{2^n times 2^1 times 2}{2^n} = 2 times 2 = 4)