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15
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Show that a polynomial vanishes

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#polynomials #binomial-coefficients #stirling-numbers
73
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Binomial identity $\sum\limits_{k=1}^{n-1}(-1)^{k+1}\frac{n-1 \choose k}{n-k} = \frac 2 n$

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#binomial-coefficients
33
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How to compute $\log\binom {n_H + n_T}{n_H}$?

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#logarithms #binomial-coefficients
102
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Stirling number of second kind and binomial coefficients, how to prove equality?

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#proof-writing #binomial-coefficients #generating-functions #stirling-numbers
414
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An interesting problem of polynomials

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#polynomials #binomial-coefficients #binomial-theorem
80
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Proof by calculation binomial coefficient

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#combinatorics #inequality #binomial-coefficients
102
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Compute Taylor Series $\ln(x^2-x+1)$

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#real-analysis #combinatorics #taylor-expansion #binomial-coefficients
95
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Bounding Euler's e by showing $2 \leq \left (1+ \frac{1}{n}\right)^n < 3$

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#inequality #binomial-coefficients #binomial-theorem
692
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How many non-negative integer solutions exist for: $x+y+z=48$ where, $x<y<z$?

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#combinatorics #number-theory #permutations #binomial-coefficients
76
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Limit of the binomial coefficients

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#real-analysis #functional-analysis #limits #binomial-coefficients
239
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Binomial coefficient (7 choose 3)=Binomial coefficient (7 choose x)

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#binomial-coefficients #factorial
531
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Solve binomial coefficient equation

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#binomial-coefficients #problem-solving #factorial
27
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Checking a newtonian binomial expansion

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#algebra-precalculus #binomial-coefficients #binomial-theorem
120
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Evaluating the sum $\sum_{k=0}^n (-1)^k \binom{2n+1}{n+k+1}$

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#combinatorics #summation #binomial-coefficients
306
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Is there a closed form for $\int_0^1\frac{\ln(x) \sin^{-1}(x)}{x\sqrt{1-x^2}}dx\ ?$

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#calculus #integration #sequences-and-series #binomial-coefficients #polylogarithm

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