Two and two makes how many?

Algebra Level 2

2 n − 2 n − 1 = ? \large 2^{n} - 2^{n-1} =?

2 n 2^{n} 2 n − 1 2^{n-1} 1 1 0 0 2 n / 2 2^{n/2} 2 2

Abhilasha Supe by Abhilasha Supe , 18, India

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4 solutions

Chew-Seong Cheong
Jul 27, 2018

2 n − 2 n − 1 = 2 n − 1 ( 2 − 1 ) = 2 n − 1 2^n-2^{n-1}=2^{n-1}(2-1)=\boxed{2^{n-1}}

4 Helpful 0 Interesting 1 Brilliant 0 Confused
Vin Benzin
Jul 26, 2018

A way of rewriting it. 2*2^(n-1)-2^(n-1)

1 Helpful 1 Interesting 0 Brilliant 0 Confused
Munem Shahriar
Jul 26, 2018

2 n − 2 n − 1 = 2 n − 2 n ⋅ 2 − 1 = 2 n ( 1 − 1 2 ) = 2 n 2 = 2 n − 1 2^n -2^{n-1} = 2^n - 2^n \cdot 2^{-1} = 2^n\left(1 - \frac12\right) = \dfrac{2^n}{2} = 2^{n-1}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

2 n − 2 n − 1 = 2 n − 2 n 2 = 2 n ( 1 − 1 2 ) = 2 n ( 1 2 ) = 2 n 2 = 2 n − 1 2^n-2^{n-1}=2^n-\dfrac{2^n}{2}=2^n\left(1-\dfrac{1}{2}\right)=2^n\left(\dfrac{1}{2}\right)=\dfrac{2^n}{2}=\large{\color{#69047E}\boxed{2^{n-1}}}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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