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Question Number 121339 by Eric002 last updated on 06/Nov/20

prove that   ((n),(1) )+ ((n),(4) )+ ((n),(7) )+....=(1/3)(2^n +2cos(((n−2)π)/3))

$${prove}\:{that} \\ $$$$\begin{pmatrix}{{n}}\\{\mathrm{1}}\end{pmatrix}+\begin{pmatrix}{{n}}\\{\mathrm{4}}\end{pmatrix}+\begin{pmatrix}{{n}}\\{\mathrm{7}}\end{pmatrix}+....=\frac{\mathrm{1}}{\mathrm{3}}\left(\mathrm{2}^{{n}} +\mathrm{2}{cos}\frac{\left({n}−\mathrm{2}\right)\pi}{\mathrm{3}}\right)\: \\ $$

Answered by mindispower last updated on 06/Nov/20

whst is   the logique  Σ_k  ((n),((g(k))) ),what is g(k)

$${whst}\:{is}\: \\ $$$${the}\:{logique} \\ $$$$\underset{{k}} {\sum}\begin{pmatrix}{{n}}\\{{g}\left({k}\right)}\end{pmatrix},{what}\:{is}\:{g}\left({k}\right) \\ $$$$ \\ $$

Commented by Eric002 last updated on 06/Nov/20

there was a typo i corrected it

$${there}\:{was}\:{a}\:{typo}\:{i}\:{corrected}\:{it}\: \\ $$

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