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How to evaluate the sum of infinite series numerically?

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#sequences-and-series #summation #numerical-methods
95
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Show that $\sum\limits_{r=1}^n\sum\limits_{k=1}^{n-r+1}(2r-1)k=\frac 13\sum\limits_{r=1}^nr\sum\limits_{s=1}^{n+1}s$

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#summation
629
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How could I go about proving this summation of a rising factorial?

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#combinatorics #discrete-mathematics #summation #induction
202
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Sum over Subadditive functions

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#summation
140
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Evaluate $\sum_{k=2}^\infty{\frac{(-1)^k}{\ln k}}$

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#integration #definite-integrals #summation #special-functions
76
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How to calculate the cardinality of following set

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#group-theory #summation #finite-fields #cardinals #primitive-roots
53
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Derivation of $\frac{1}{{p}_{1}\, {p}_{2}\, \cdots\, {p}_{m}} \prod\limits_{i = 1}^{m} \left({{p}_{i} - 1}\right)$ from reciprocal sum expansion

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#summation #inclusion-exclusion
60
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Sum of combinations of sets

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#combinatorics #summation
884
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Prove inequality $\sum_{k=1}^{n}\frac{a_kb_k}{a_k+b_k}\le \frac{AB}{A+B}$

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#inequality #summation #induction #fractions #cauchy-schwarz-inequality
92
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What's the summation of a square root of a quadratic function?

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#summation
42
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Confusion in proof regarding the summation operator

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#summation
101
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Prove sequences {$a_n$} {$b_n$} of complex numbers converge

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#real-analysis #sequences-and-series #limits #convergence-divergence #summation
218
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Closed form expression of odd series

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#summation #closed-form
50
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A recurrence relation where the next term is related by the sum of previous pair product terms

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#summation #recurrence-relations #products
71
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How to determine the value of $\sum_{k = 0}^{r} \binom{n + k - 1}{k}$?

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#combinatorics #summation

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