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