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Expansion using Pascal's triangle

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#binomial-theorem
26
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Find $\sum_{n=0}^k \frac{C_n^k A^n B^{k-n} n!}{(\frac{n}{2})!}$.

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#sequences-and-series #convergence-divergence #binomial-theorem
277
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Use binomial theorem to calculate n power of a sum (MIT Single Variable Calculus)

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#binomial-theorem
611
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What is the coefficient of x^9 y^16 in the expansion of (7x+21y)^25

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#binomial-coefficients #binomial-theorem
3.2k
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What is the coefficient of the term $x^4 y^5$ in $(x+y+2)^{12}$?

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#combinatorics #discrete-mathematics #binomial-coefficients #binomial-theorem
99
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Try to solve Binomial Distribution

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#binomial-coefficients #binomial-theorem
177
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How to show that $\sum\limits_{k=0}^{\lfloor0.999n\rfloor}\binom{2n}{k} < \binom{2n}{n} $ holds for large n

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#discrete-mathematics #summation #binomial-coefficients #binomial-theorem
177
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Binomial Theorem Identity

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#binomial-coefficients #binomial-theorem
124
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solving a sequence problem

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#sequences-and-series #binomial-theorem
303
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Proving $(x+y)^n=x^n+y^n$

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#binomial-theorem
250
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If $a_n+b_n\sqrt{3}=(2+\sqrt{3})^n$, then what's $\lim_{n\rightarrow\infty}\frac{a_n}{b_n}$?

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#limits #binomial-theorem
63
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$\sum_{i=1}^{n}i^k=\sum_{i=1}^{k}\frac{c_{k+1-i}k!}{i!}n^i$. What is known about $\{c_k\}_{k=0}^{\infty}$?

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#reference-request #summation #binomial-coefficients #factorial #binomial-theorem
76
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How can I prove this relation (combinatorics)

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#combinatorics #binomial-theorem #inclusion-exclusion
2.5k
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binomial expansion for negative and fractional powers

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#combinatorics #binomial-coefficients #binomial-theorem #negative-binomial
102
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Find values: $ \sum_{k=1}^{15}k{15\choose k}\Big(\frac{1}{20}\Big)^k\Big(\frac{19}{20}\Big)^{15-k}$ and same one but with $k^2$

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#binomial-coefficients #binomial-theorem

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