Formula q_850 (Q657): Difference between revisions

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Created claim: arqmath formula id (P8): q_850
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Created claim: Defining formula (P1): \sum_{k=0}^{n}k\cdot \left(\begin{array}{l}{n}\\{k}\end{array}\right)\leq \sum_{k=0}^{n}k\cdot \left(\begin{array}{l}{n}\\{\lfloor \frac{n}{2}\rfloor}\end{array}\right)\leq \frac{n\cdot(n+1)}{2}\cdot \left(\begin{array}{l}{n}\\{\lfloor \frac{n}{2}\rfloor}\end{array}\right)\leq n(n+1)! \leq nn^n \leq n^{n+1}
 
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\sum_{k=0}^{n}k\cdot \left(\begin{array}{l}{n}\\{k}\end{array}\right)\leq \sum_{k=0}^{n}k\cdot \left(\begin{array}{l}{n}\\{\lfloor \frac{n}{2}\rfloor}\end{array}\right)\leq \frac{n\cdot(n+1)}{2}\cdot \left(\begin{array}{l}{n}\\{\lfloor \frac{n}{2}\rfloor}\end{array}\right)\leq n(n+1)! \leq nn^n \leq n^{n+1}
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