# equation involving addition of powers

Printable View

• November 28th 2011, 08:05 PM
Jskid
equation involving addition of powers
Show that $2^k+2^k-1=2^{k+1}-1$
• November 28th 2011, 08:14 PM
Prove It
Re: equation involving addition of powers
Quote:

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*}
• November 28th 2011, 08:18 PM
Jskid
Re: equation involving addition of powers
Quote:

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.
• November 28th 2011, 08:56 PM
Prove It
Re: equation involving addition of powers
Quote:

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.