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Show $\sum_{k=1}^{2n-1}\frac{\left(-1\right)^{k-1}k}{\binom{2n}{k}}=\frac{n}{n+1}$

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#discrete-mathematics #summation #binomial-coefficients
612
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Possible formula for $\sum_{} (\alpha\beta)^2$ and $\sum_{} \alpha\beta(\alpha+\beta)$

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#polynomials #summation #roots #quartics
4.1k
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Prove the maximum value of entropy function

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#probability #summation #solution-verification #information-theory #entropy
37
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Reason why $\sum_{j=0}^{\infty} \sum_{k=0}^j a_{k,j-k} =\sum_{j=0}^{+\infty} \sum_{k=0}^{\infty} a_{k,j}$

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#sequences-and-series #summation #index-notation
117
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Show $\sum_{k=0}^{n}2^{n-k}\binom{a+k}{k}\frac{a-k}{a+k}=\binom{a+n}{n}$

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#discrete-mathematics #summation #binomial-coefficients
157
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Identity related to $\sum_{k=0}^{n}\frac{x^k}{\binom{n}{k}}$

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#discrete-mathematics #summation #binomial-coefficients
56
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How can I find a simple upper bound for this sum?

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#sequences-and-series #summation #power-series #upper-lower-bounds
357
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Improve upper bound for double sum

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#real-analysis #calculus #summation #upper-lower-bounds
406
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Convolution of $l^2$ functions is not an $l^2$ function.

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#summation #convolution
35
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Decreasing summation amount based on number selected

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#summation #summation-method
53
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How to find the sum of n natural logarithms that are cubed?

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#summation #logarithms
119
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Multinomial expansion sum

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#summation #generating-functions #geometric-series
55
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How to show that sum is upper bounded by integral

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#inequality #definite-integrals #summation #upper-lower-bounds
106
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Evaluate $\sum_{r=1}^{\infty} \frac{1 \cdot 3 \cdot \ldots (2r-1)}{r!}\left(\frac{2}{5} \right)^{r}$

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#integration #sequences-and-series #summation #taylor-expansion #fubini-tonelli-theorems
38
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Finite Geometric Series Scaled by Binomial Coefficients

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#summation #binomial-coefficients #geometric-series

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