https://math.codidact.com/categories/41/tags/5422.rssNew Posts Tagged 'summation' - MathematicsMathematics - Codidact2023-05-29T10:38:46Zhttps://math.codidact.com/posts/288168Closed-form expression for sum of Modulo Arithmetic Progressiontheabbiehttps://math.codidact.com/users/537872023-05-28T16:41:05Z2023-05-29T10:38:46Z<p>Is there any closed-form expression or at least an efficient way to calculate this sum?</p>
$$ \sum_{i=1}^{N} (a \cdot i) \bmod{M} $$<p>we can assume $N$, $a$, and $M$ are large enough such tha...https://math.codidact.com/posts/285680How can a 15 year old construe the LHS of Generalized Vandermonde's Identity, when it lacks summation limits and a summation index?DNBhttps://math.codidact.com/users/536282022-01-25T06:07:44Z2022-01-25T19:24:52Z<p>Paradoxically, though <a href="https://math.stackexchange.com/q/3572304">Rothe-Hagen Identity</a> (henceforth RHI)</p>
<p>$\sum\limits_{k=0}^n\frac{x}{x+kz}{x+kz \choose k}\frac{y}{y+(n-k)z}{y+...https://math.codidact.com/posts/282644How does the change of variable $\color{red}{r↦n−r}$ transmogrify $\sum\limits_{r=0}^n2^{n-r}\binom{n+r}{n}=2^{2n}$ into $\sum\limits_{k=0}^{n} \frac{\binom{2n-k}{n}}{2^{2n-k}}=1$?DNBhttps://math.codidact.com/users/536282021-07-11T06:25:22Z2021-07-11T19:45:24Z<p>I'm unskilled at performing algebra with Capita-sigma notation. <a href="https://math.stackexchange.com/questions/2219125/prove-using-combinatorics-sum-limits-r-0n2n-r-binomnrn-22n?rq=1#comment4...