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Sum of coefficients of even powers of x in $(1+x)^5 (1+x^2)^5$?

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#combinatorics #binomial-coefficients #binomial-theorem #combinatorial-proofs
663
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Math Olympiad (Binomial coefficient)

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#contest-math #binomial-theorem
56
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How is $ C_0^n+\frac{1}{2}(C_0^n-C_1^n)+\frac{1}{3}(C_0^n-C_1^n+C_2^n)+.. =C_0^{n-1}+\frac{1}{2}C_1^{n-1}(-1)+\frac{1}{3}C_2^{n-1}(-1)^2... $?

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#binomial-coefficients #binomial-theorem
56
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Proving the Hockey Stick Identity with the Summation Identity

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#combinatorics #binomial-coefficients #binomial-theorem
616
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Upper bound of of powers of a binomial

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#binomial-theorem #upper-lower-bounds
4.8k
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How many digits is $99^{99}$ without a calculator?

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#algebra-precalculus #logarithms #binomial-theorem
154
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Which one is greater (A or B)?

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#binomial-theorem #number-comparison
251
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How can I prove the following equality?

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#combinatorics #summation #binomial-coefficients #binomial-theorem
683
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Proving $\sum\limits_{k=0}^{\infty}\binom {m-r+s}k\binom {n+r-s}{n-k}\binom {r+k}{m+n}=\binom rm\binom sn$

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#sequences-and-series #binomial-coefficients #binomial-theorem
67
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How can I find a short term for those sums?

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#combinatorics #binomial-coefficients #binomial-theorem #binomial-distribution
196
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Prove the Binomial Theorem using induction (What is mathematics book)

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#induction #binomial-theorem
74
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Combinatorics Binomial How to prove it?

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#binomial-coefficients #binomial-theorem
76
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Expansion question involving Taylor or Binomial series?

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#taylor-expansion #binomial-theorem
309
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Sum of independent Poisson distributions and binomial theorem

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#convolution #binomial-theorem #poisson-distribution
323
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Prove the following Combinatorial Identity:

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#combinatorics #binomial-theorem

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