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Summation of binomial coefficients multiplied by their index

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#combinatorics #binomial-coefficients #binomial-theorem #geometric-progressions
75
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Summation of binomial coefficients upon $(r+2)$

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#combinatorics #binomial-coefficients #binomial-theorem
528
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Generating function, N coin tosses: Find the probability that the total number of heads is a) even b) divisible by 3.

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#probability #probability-theory #probability-distributions #generating-functions #binomial-theorem
111
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Value of Number(1- fractional part)

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#combinatorics #binomial-coefficients #binomial-theorem
120
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Verifying Newton's Binomial Series for $(1+x)^{−2}$

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#calculus #sequences-and-series #generating-functions #binomial-theorem
50
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Squaring a Binomial

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#binomial-coefficients #binomial-theorem
46
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On the number of subsets of a finite set with size in different congruence class of $3$

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#combinatorics #trigonometry #binomial-theorem
1.1k
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Correct way of determining the range of validity when expanding (1+f(x))^n

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#convergence-divergence #binomial-theorem
197
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The probability of observing the mean draw from binomial distribution

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#probability #probability-theory #probability-distributions #binomial-theorem
94
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Why does $\int_0^1\binom{2n}{n}x^n(1-x)^ndF(x)=\frac{1}{2n+1}$?

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#probability #integration #binomial-theorem #binomial-distribution
253
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If I ask $2N$ people a yes or no question, what's the probability $N$ say yes?

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#probability-theory #probability-distributions #binomial-coefficients #binomial-theorem #beta-function
18
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A question about how to factorise a binomial.

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#binomial-theorem
90
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Ways of choosing ice-cream scoops - intuition/further explanation

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#combinatorics #binomial-coefficients #binomial-theorem
219
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find $\sum_{k=0}^{n}(-1)^k\binom{n}{k}^2$

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#combinatorics #summation #binomial-theorem
46
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Proof: $(a^2+h)^{1/2} \approx a+\frac{h}{2a}$ for $0<h<a^2$

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#number-theory #elementary-number-theory #binomial-theorem

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