1. ## equation involving addition of powers

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

2. ## Re: equation involving addition of powers

Originally Posted by Jskid
Show that $\displaystyle 2^k+2^k-1=2^{k+1}-1$
\displaystyle \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*}

3. ## Re: equation involving addition of powers

Originally Posted by Prove It
\displaystyle \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.

4. ## Re: equation involving addition of powers

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.