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Prove $\sum^{n}_{i=1}\binom{n}{i}i=n2^{n-1}$ using binomial and induction

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#induction #binomial-theorem
186
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Use the binomial theorem to prove that for $n$ a positive integer the following holds

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#algebra-precalculus #self-learning #binomial-theorem
366
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Proving the binomial series for all real (complex) n using Taylor series

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#combinatorics #taylor-expansion #binomial-theorem
103
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Find sum of nasty series containing Binomial Coefficients

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#binomial-coefficients #binomial-theorem
70
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Value of $a_2+a_6+a_{10}+\cdots+a_{42}$

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#sequences-and-series #algebra-precalculus #binomial-theorem
49
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Definite sum for $(1+a)^n$

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#functions #exponentiation #binomial-theorem
76
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How to prove $\sum_{r=1}^{n} r^{2}\binom {n} {r} = n(n+1)2^{n-2}$?

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#binomial-theorem
50
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Binomial Theorem Question $1+(1+x)+(1+x)^2+\dots+(1+x)^n$

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#binomial-coefficients #binomial-theorem
485
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Distinct terms in a binomial expansion

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#polynomials #binomial-theorem
68
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Limit of a sequence (binomial series and generating function for Catalan)

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#sequences-and-series #convergence-divergence #binomial-theorem
68
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How to show that inequality of a combinatoric series holds true

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#combinatorics #binomial-theorem #multinomial-theorem
51
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Best way to solve for $(1+a)^{-n}=1-\frac{I}{C}a$

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#approximation #binomial-theorem
169
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Can we express a binomial expansion where the index is negative or not an integer using summation and Pi notation?

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#binomial-theorem
172
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Probability:Binomial Distribution Mean and Variance Problem

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#probability #probability-theory #probability-distributions #binomial-theorem #binomial-distribution
218
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The best way to approximate $15^{1/4}$

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#roots #approximation #binomial-theorem #newton-raphson

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