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Expand$\frac{ x^{k+1}}{k+1} -\frac{ (x-1)^{k+1}}{k+1} $using the binomial theorem

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#sequences-and-series #polynomials #proof-verification #binomial-theorem
80
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Suppose that for all $i \le k$, one knows a polynomial $f_i$ such that $f_i(x) = x^i$, calculate $f_{k+1}$

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#sequences-and-series #polynomials #summation #binomial-theorem
189
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coefficient of $x^9$ in binominal expansion

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#binomial-coefficients #binomial-theorem
32
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Binomial equation

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#combinatorics #binomial-theorem
45
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Counting functions and subsets

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#binomial-coefficients #binomial-theorem #divisor-counting-function
89
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Find the co-efficient of $x^3y^3zw^2$ in the expression of $(x-y+2z-2w)^9$.

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#binomial-theorem
1.2k
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sum of even binomial coefficients

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#binomial-coefficients #combinations #binomial-theorem
51
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Proving an equality with binomials

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#binomial-coefficients #binomial-theorem
121
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Coefficient of $x^{-2}$ in expression $(x-1/x)^{12}$

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#binomial-coefficients #binomial-theorem
254
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Find the last digit of $7^{802} -3^{683}$

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#modular-arithmetic #binomial-theorem
1.7k
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Prove the inequality using the binomial theorem

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#inequality #binomial-theorem
121
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find the value of $\sum_{n=0}^{2016} \frac{\left ( -1 \right )^{n} a_{n}}{4n+1}$ (details inside)

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#number-theory #binomial-coefficients #binomial-theorem
1.7k
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Bernoulli trials and permutations

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#probability #binomial-theorem
163
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Compute $\lim_{n\to\infty} (1+n+n^2)^{\frac{1}{n}}$.

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#limits #binomial-theorem
386
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Index Shifting & Simplifying Taylor Expansion

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#power-series #binomial-theorem

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