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How to derive these inequalities?

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#inequality #summation #arithmetic #induction
934
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A sum of Laguerre polynomials

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#polynomials #summation #binomial-coefficients #orthogonal-polynomials
154
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Proving that mean KDR in a videogame is one

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#summation #proof-writing #average #ratio
145
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$\prod_{i\in I}(1+x_i)=\sum_{J\subseteq I}\prod_{j\in J}x_j$

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#summation #products
49
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An inequality involving Möbius function

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#elementary-number-theory #inequality #summation #arithmetic-functions #multiplicative-function
186
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A problem of sum floors

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#summation #ceiling-and-floor-functions
4.3k
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Proving Product of Transition Matrices is again a Transition Matrix.

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#linear-algebra #probability #matrices #summation #markov-chains
516
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Integer sum as binomial coefficient

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#summation #binomial-coefficients
99
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Calculate the sum of S.

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#summation
410
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Evaluate $S=\Sigma\Sigma\Sigma x_ix_jx_k$

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#summation
72
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How to solve $\frac{1}{n}\left[1+2\sum_{k=1}^{n-1}\frac{1}{\sqrt{\frac{n}{n-k}}}\right]$

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#summation
103
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Evaluate $\displaystyle{\lim_{n\to \infty}\frac{1}{n}\sum_{r=0}^{n-1}\cos\frac{r\pi}{2n}}$

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#limits #summation
75
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What is the value of $\lim_{n\to \infty}\frac{1}{n}\sum_{i=1}^n[\sqrt\frac{4i}{n}]$

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#limits #summation
87
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Does $\sum_{i=1}^{k-1}\lceil \log_2\frac{N}{i}\rceil$ have a closed form?

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#summation #logarithms #closed-form
1.3k
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Algebraic manipulation of floors and ceilings

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#sequences-and-series #summation #ceiling-and-floor-functions

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