How to convert 3*2^(n) + 2^(2n+1) - 2^(n+1) into 2^(2n+1) + 2^(n)

Question

Hi all!

 

I'm attempting to convert: 3*2^(n) + 2^(2n+1) - 2^(n+1)

 

into: 2^(2n+1) + 2^(n)

 

^ means exponent

n is a variable

 

Does anyone have any idea on how I might go about this?

 

Thanks!

Answer 1

f(n) = (3)2ⁿ + 2²ⁿ⁺¹ - 2ⁿ⁺¹

 

Note that the 3rd term can be expressed as

 

-2ⁿ⁺¹ = -2ⁿ2¹ = (-2)2ⁿ

 

Then

 

f(n) = (3)2ⁿ + 2²ⁿ⁺¹ + (-2)2ⁿ

 

Combine the 1st and 3rd terms and get

 

f(n) = (3 - 2)2ⁿ + 2²ⁿ⁺¹ = 2ⁿ + 2²ⁿ⁺¹

 

f(n) = 2²ⁿ⁺¹ + 2ⁿ