Question

Coefficient of $x^n$ in $(x^2+3x+2)^n$

score 137 · Answer 1 · 2026-03-26 01:34:55

137

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Coefficient of $x^n$ in $(x^2+3x+2)^n$

Published on 26 Mar 2026 - 1:34

score 43 · Answer 2 · 2020-07-19 05:59:23

43

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The sum of combination $ \sum _{i \equiv q \pmod p} {n \choose i}$

Published on 19 Jul 2020 - 5:59

score 166 · Answer 3 · 2020-07-19 09:53:09

166

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How to evaluate $\int x^5 (1+x^2)^{\frac{2}{3}}\ dx$?

Published on 19 Jul 2020 - 9:53

score 100 · Answer 4 · 2020-07-21 05:24:43

100

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Computing $2 \binom{n}{0} + 2^2 \frac{\binom{n}{1}}{2} + 2^3 \frac{\binom{n}{2}}{3} + \cdots + 2^{n+1} \frac{\binom{n}{n}}{n+1}$

Published on 21 Jul 2020 - 5:24

score 106 · Answer 5 · 2020-07-23 10:42:07

106

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Remainder when $^{40}C_{12}$ is divided by $7$.

Published on 23 Jul 2020 - 10:42

score 57 · Answer 6 · 2020-07-23 15:37:13

57

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prove that $\binom{k+1}{1} S_k(n)+\binom{k+1}{2} S_{k-1}(n)+.........+\binom{k+1}{k+1} S_0(n)=(n+1)^{k+1}-1$

Published on 23 Jul 2020 - 15:37

score 100 · Answer 7 · 2020-07-24 00:15:07

100

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For $p\in (0, 1)$ and $n\rightarrow \infty$, how do I evaluate a general term in the binomial expansion of $(p+1-p)^n$?

Published on 24 Jul 2020 - 0:15

score 452 · Answer 8 · 2026-03-25 04:39:22

452

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How to use Euler-Maclaurin summation to show the following relationship over Gamma function

Published on 25 Mar 2026 - 4:39

score 460 · Answer 9 · 2020-07-25 14:26:03

460

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Find $\sum_{r=1}^{3n-1}{ (-1)^{r-1}r\over{3n \choose r}}$, if $n$ is even

Published on 25 Jul 2020 - 14:26

score 180 · Answer 10 · 2020-07-27 03:10:03

180

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Taylor Series Expansion of an Arbitrary Function to an Arbitrary Power

Published on 27 Jul 2020 - 3:10

score 80 · Answer 11 · 2020-07-28 23:57:00

80

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Probability of observing success with dependent numbers and a custom rule?

Published on 28 Jul 2020 - 23:57

score 460 · Answer 12 · 2020-07-29 08:54:56

460

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Find $a$, $b$ such that $x^2 - x -1$ is a factor of $ax^9 + bx^8 + 1$

Published on 29 Jul 2020 - 8:54

score 254 · Answer 13 · 2020-07-30 05:54:53

Prove that $\binom{n}{0}\binom{n+1}{n} +\binom{n}{1}\binom{n}{n-1} +\binom{n}{2}\binom{n-1}{n-2} +\cdots +\binom{n}{n}\binom{1}{0} = 2^{n-1}(n+2)$

score 89 · Answer 14 · 2020-07-30 10:57:23

If $y = \frac{2}{5}+\frac{1\cdot3}{2!} \left(\frac{2}{5}\right)^2+\frac{1\cdot3\cdot5}{3!} \left(\frac{2}{5}\right)^3+\cdots$, find $y^2+2y$

score 118 · Answer 15 · 2020-07-30 20:12:10

118

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Proof that $(1 + t)^n = \sum\limits_{k = 0}^{n} \binom{n}{k} t^k$

Published on 30 Jul 2020 - 20:12

List Question

Coefficient of $x^n$ in $(x^2+3x+2)^n$

The sum of combination $ \sum _{i \equiv q \pmod p} {n \choose i}$

How to evaluate $\int x^5 (1+x^2)^{\frac{2}{3}}\ dx$?

Computing $2 \binom{n}{0} + 2^2 \frac{\binom{n}{1}}{2} + 2^3 \frac{\binom{n}{2}}{3} + \cdots + 2^{n+1} \frac{\binom{n}{n}}{n+1}$

Remainder when $^{40}C_{12}$ is divided by $7$.

prove that $\binom{k+1}{1} S_k(n)+\binom{k+1}{2} S_{k-1}(n)+.........+\binom{k+1}{k+1} S_0(n)=(n+1)^{k+1}-1$

For $p\in (0, 1)$ and $n\rightarrow \infty$, how do I evaluate a general term in the binomial expansion of $(p+1-p)^n$?

How to use Euler-Maclaurin summation to show the following relationship over Gamma function

Find $\sum_{r=1}^{3n-1}{ (-1)^{r-1}r\over{3n \choose r}}$, if $n$ is even

Taylor Series Expansion of an Arbitrary Function to an Arbitrary Power

Probability of observing success with dependent numbers and a custom rule?

Find $a$, $b$ such that $x^2 - x -1$ is a factor of $ax^9 + bx^8 + 1$

Prove that $\binom{n}{0}\binom{n+1}{n} +\binom{n}{1}\binom{n}{n-1} +\binom{n}{2}\binom{n-1}{n-2} +\cdots +\binom{n}{n}\binom{1}{0} = 2^{n-1}(n+2)$

If $y = \frac{2}{5}+\frac{1\cdot3}{2!} \left(\frac{2}{5}\right)^2+\frac{1\cdot3\cdot5}{3!} \left(\frac{2}{5}\right)^3+\cdots$, find $y^2+2y$

Proof that $(1 + t)^n = \sum\limits_{k = 0}^{n} \binom{n}{k} t^k$

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