equation involving addition of powers

**Jskid** · November 28th 2011, 08:05 PM

Show that $2^k+2^k-1=2^{k+1}-1$

**Prove It** · November 28th 2011, 08:14 PM

Originally Posted by Jskid

Show that $2^k+2^k-1=2^{k+1}-1$

$\displaystyle \begin{align*} 2^k + 2^k - 1 &= 2\cdot 2^k - 1 \\ &= 2^1 \cdot 2^k - 1 \\ &= 2^{k + 1} - 1 \end{align*}$

**Jskid** · November 28th 2011, 08:18 PM

Originally Posted by Prove It

$\displaystyle \begin{align*} 2^k + 2^k - 1 &= 2\cdot 2^k - 1 \\ &= 2^1 \cdot 2^k - 1 \\ &= 2^{k + 1} - 1 \end{align*}$

The very first equality is not apparent to me.

**Prove It** · November 28th 2011, 08:56 PM

Originally Posted by Jskid

The very first equality is not apparent to me.

n + n = 2n

Here your n just happens to be 2^k.

Thread: equation involving addition of powers