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What is the range of convergence of $\sum_{n=0}^{\infty} {(-1)}^n\binom{1/2}{n}\frac{1}{2n+3}.$

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#sequences-and-series #convergence-divergence #definite-integrals #binomial-theorem
613
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The relationship between the Pascal's triangle/sequence and the binomial number theorem?

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#sequences-and-series #binomial-coefficients #binomial-theorem
65
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Is it possible to extract a variable out of a bounded sum of binomial coefficients

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#summation #binomial-coefficients #binomial-theorem
453
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Multinomial theorem & combinatorial probabilities

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#probability #combinatorics #binomial-theorem #multinomial-coefficients
40
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A curve C has an equation of $y = f(x)$, where $ f(x) = \frac{4x}{\sqrt{4+x}+\sqrt{4-x}} $, and $ -4\le x\le4. $

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#binomial-theorem
932
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Remainder on division with $22$

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#number-theory #elementary-number-theory #modular-arithmetic #divisibility #binomial-theorem
75
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Problem using binominal theorem?

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#elementary-number-theory #binomial-theorem #integers #natural-numbers
45
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Evaluating the variance of the biinomial distribution directly

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#probability #statistics #summation #binomial-coefficients #binomial-theorem
110
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Question wrt Binomial theorem

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#algebra-precalculus #combinations #binomial-theorem
691
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Derivation of Binomial theorem

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#binomial-coefficients #binomial-theorem
70
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Simplify and compute the MGF of $[1-(1-(1-e^{-ax})^{N_1})(1-(1-e^{-ax})^{N_2})]^{M-1} $

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#binomial-theorem #moment-generating-functions
126
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Coefficient of $x^k$ in ${(1 - e^x)}^{-n}$

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#sequences-and-series #taylor-expansion #exponential-function #binomial-theorem
77
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How to simplify $\sum _{l=1} ^{k} \sum_{j_1 \ge 1} \cdots \sum_{j_l \ge 1, j_1 + \cdots + j_l=k} \binom{k}{j_1 \cdots j_l} \binom{-2}{l} 2^l$

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#binomial-theorem #moment-generating-functions
481
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Proof that $\sum\limits _{n=1}^{\infty } n\sum\limits _{j=2}^{\infty }{\frac {(-1)^{j-1}}{j^2} \left( 1-{j}^{-1} \right)^{n-1}} = -\frac12$

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#sequences-and-series #taylor-expansion #binomial-coefficients #riemann-zeta #binomial-theorem
1.8k
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Why binomial expansion approximation works?

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#binomial-theorem

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