Ham Radio Deluxe 6 Crack Torrent
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This site may contain links to other web sites, of whom Williams Communications Inc. is not responsible.Q:
Sum of coefficients of binary expansion of $5^{17}$
How to prove that $\sum_{j=0}^{16} (-1)^{j}5^j =0$?
I had proved it by factoring $17$ as $2 \cdot 2 \cdot 5 \cdot 5 \cdot 13$ and then summing it up but it seemed very long-winded. Can this be proved by some shortcut?
A:
With $17=2\cdot 5+5\cdot 13$, you can use the fact that
$$ \sum_{j=0}^k (-1)^j a^{2^j} = 0$$
if $k$ is the number of bitwise right shifts applied to $a$.
A:
Let $a_j=\sum_{m=0}^j (-1)^m 5^m$. Then $$a_{17}=0+\cdots+0-1^0+0+\cdots+0+1^1+\cdots+1^0+\cdots.$$ Now if $n=2^k$ for some $k$, you have $$a_{n+1}=a_n+n5^0+\cdots+5^0-1^0+\cdots-1^ https://virtualanalytics.ai/pdf-studio-viewer-torrent-activation-code-april-2022/
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