List questions from binomial-theorem

Published on 06 Jun 2015 - 22:25

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Factoring $a^{k} - b^{k}$

Published on 07 Jun 2015 - 20:17

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How many ways to distribute $n$ objects into $r$ boxes so that each box have at least $1$ (but no more than $k$) objects?

Published on 31 Mar 2026 - 12:16

437

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Number-theory proof involving the Binomial Theorem

Published on 11 Jun 2015 - 3:31

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Binomial product expansion

Published on 19 Jun 2015 - 12:08

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Finding a closed form expression for $\sum_{k=\frac {n+2} 2} ^n \binom n k$

Published on 19 Jun 2015 - 19:57

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Problem with this challenging summation

Published on 20 Jun 2015 - 15:08

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prove that $(1+pt)^{p^{r-1}} \equiv 1 \pmod {p^r}$

Published on 29 Mar 2026 - 8:21

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Binomial expansion in descending power

Published on 22 Jun 2015 - 7:57

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$1+\sqrt[3]{e^{2a}}\sqrt[5]{e^{b}}\sqrt[15]{e^{2c}} \leq \sqrt[3]{(1+e^{a})^2}\sqrt[5]{1+e^{b}}\sqrt[15]{(1+e^{c})^2}$

Published on 22 Jun 2015 - 9:20

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Prove limit converges in definition of $e.$

Published on 22 Jun 2015 - 12:05

147

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Show $\sum_{ r = 0}^{n} {(\binom n r)}^{2} = \frac{(2n)!}{(n!)^{2}}$

Published on 23 Jun 2015 - 6:09

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How to find coefficient of $x^{12}$ in the expansion of $(1+x+x^2+x^3+...+x^n)^4$

Published on 23 Jun 2015 - 19:02

948

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Find the remainder of the following using binomial theorem?

Published on 24 Jun 2015 - 5:27

475

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What are the last two digits of $77^{17}$?

Published on 30 Mar 2026 - 20:43

List Question

The convergence of the binomial expansion

Factoring $a^{k} - b^{k}$

How many ways to distribute $n$ objects into $r$ boxes so that each box have at least $1$ (but no more than $k$) objects?

Number-theory proof involving the Binomial Theorem

Binomial product expansion

Finding a closed form expression for $\sum_{k=\frac {n+2} 2} ^n \binom n k$

Problem with this challenging summation

prove that $(1+pt)^{p^{r-1}} \equiv 1 \pmod {p^r}$

Binomial expansion in descending power

$1+\sqrt[3]{e^{2a}}\sqrt[5]{e^{b}}\sqrt[15]{e^{2c}} \leq \sqrt[3]{(1+e^{a})^2}\sqrt[5]{1+e^{b}}\sqrt[15]{(1+e^{c})^2}$

Prove limit converges in definition of $e.$

Show $\sum_{ r = 0}^{n} {(\binom n r)}^{2} = \frac{(2n)!}{(n!)^{2}}$

How to find coefficient of $x^{12}$ in the expansion of $(1+x+x^2+x^3+...+x^n)^4$

Find the remainder of the following using binomial theorem?

What are the last two digits of $77^{17}$?

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