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Tricky question involving binomial expansion

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#algebra-precalculus #binomial-coefficients #binomial-theorem
59
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want to check answer given in my book is correct or not

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#taylor-expansion #generating-functions #binomial-theorem
450
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Simplify the expression $\binom{n}{0}+\binom{n+1}{1}+\binom{n+2}{2}+\cdots +\binom{n+k}{k}$

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#algebra-precalculus #binomial-coefficients #binomial-theorem
121
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Proof of identity via binomial theorem

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#combinatorics #trees #binomial-theorem
389
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Finding binomial coefficients of product of two binomials

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#combinatorics #binomial-coefficients #binomial-theorem
520
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Use Binomial Theorem to find the remainder of $32^{{32}^{32}}$

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#binomial-theorem
53
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Finding the value of an expression using substitution

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#proof-verification #binomial-theorem #substitution
522
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Generalization of the q-Binomial Theorem

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#number-theory #binomial-coefficients #binomial-theorem #q-analogs
37
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Puzzling Trinomials and validity

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#sequences-and-series #power-series #binomial-theorem
129
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How can I analytically solve the factorial problem n! = k

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#permutations #combinations #factorial #binomial-theorem
684
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Proving Pascal's Identity algebraically, stuck with simplification

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#combinatorics #proof-verification #binomial-coefficients #binomial-theorem
193
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Is it possible a closed expression for $1^k + 2^k + ... + n^k$? If so, am I on the way?

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#summation #induction #binomial-coefficients #binomial-theorem
163
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Find the coefficient of the term $x^2$ in $\left(x+\frac 2x\right)^{4}$

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#binomial-coefficients #binomial-theorem
271
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Why in the binomial expansion are the powers of x positive?

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#binomial-theorem
117
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How many times do I have to expand?

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#binomial-theorem

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