# Sum of <munderover> &#x2211;<!-- ∑ --> <mrow class="MJX-TeXAtom-ORD"> n

Sum of $\sum _{n=1}^{N}\mathrm{cos}\left(kx-\omega t+n\theta \right)$
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Caiden Barrett
$\begin{array}{rl}\sum _{n=1}^{N}\mathrm{cos}\left(n\phantom{\rule{thinmathspace}{0ex}}\theta +a\right)& =\sum _{n=1}^{N}\left(\mathrm{cos}\left(n\phantom{\rule{thinmathspace}{0ex}}\theta \right)\mathrm{cos}a-\mathrm{sin}\left(n\phantom{\rule{thinmathspace}{0ex}}\theta \right)\mathrm{sin}a\right)\\ & =\mathrm{cos}a\sum _{n=1}^{N}\mathrm{cos}\left(n\phantom{\rule{thinmathspace}{0ex}}\theta \right)-\mathrm{sin}a\sum _{n=1}^{N}\mathrm{sin}\left(n\phantom{\rule{thinmathspace}{0ex}}\theta \right).\end{array}$