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close form solutions for infinite sums

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#sequences-and-series #summation
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Reducing summation in recurrence relation

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#summation #recurrence-relations
1.4k
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Alternating Series , why start at n = 1?

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#summation #taylor-expansion
189
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How do I express the sum $(1+k)+(1+k)^2+\ldots+(1+k)^N$ for $|k|\ll1$ as a series?

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#summation #power-series
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The coefficient of $t^n$ in $\left(\sum_{k=1}^{n-1} t^k\right)^r$

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#combinatorics #summation #generating-functions
36
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Evaluation of $\sum\limits_{i = 0}^s {\left( {\begin{array}{*{20}{c}} q \\ {{2^i}} \end{array}} \right)}$

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#summation #binomial-coefficients
46
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Further explanation regarding calculation of E[X^2]

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#probability #probability-theory #summation #random-variables
46
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How does this pattern work?

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#calculus #summation
161
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Proving binomial coefficients identity: $\binom{r}{r} + \binom{r+1}{r} + \cdots + \binom{n}{r} = \binom{n+1}{r+1}$

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#combinatorics #summation #binomial-coefficients
6.2k
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Interpretation of Ramanujan summation of infinite divergent series

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#summation #divergent-series #ramanujan-summation
104
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Show $1+2^2+...+n^n$ ≤ $(1+1/n-1)*n^n$

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#inequality #summation
1.5k
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Strict upper and lower bounds of a sum (Big-Theta)

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#convergence-divergence #definite-integrals #summation #asymptotics #ceiling-and-floor-functions
180
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Sum function operation: coefficient.

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#combinatorics #complex-numbers #summation #binomial-coefficients
504
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Show that $\sum_{n=0}^{\infty} \frac{n}{2^{n+1}} = 1$

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#sequences-and-series #summation
93
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Evaluating $\sum_{k=0}^{\infty}\frac{1-2^k}{3^k}$

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#sequences-and-series #summation

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