Question

How can I prove $\frac {d}{dx} {x^n} = n x^{n-1}$ for $ n \in \Bbb R$ without circular reasoning?

score 254 · Answer 1 · 2019-02-08 07:32:37

254

Views

How can I prove $\frac {d}{dx} {x^n} = n x^{n-1}$ for $ n \in \Bbb R$ without circular reasoning?

Published on 08 Feb 2019 - 7:32

score 185 · Answer 2 · 2026-03-25 11:04:37

185

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How can I find the coefficient of $x^6$ in $(1+x+\frac{x^2}{2})^{10}$ efficiently with combinatorics?

Published on 25 Mar 2026 - 11:04

score 1.5k · Answer 3 · 2019-02-15 11:11:42

1.5k

Views

Proving the connection between the Binomial Theorem and the product rule for derivatives

Published on 15 Feb 2019 - 11:11

score 2.2k · Answer 4 · 2019-02-18 13:23:24

In the expansion of $a{x}^3 {(2+ax)}^{11}$ , the coefficient of the term in $x^5$ is $11880$. Find the value of $a$ .

score 740 · Answer 5 · 2019-02-20 13:16:42

740

Views

Question related to Pascal Triangles and Counting Patterns

Published on 20 Feb 2019 - 13:16

score 6.9k · Answer 6 · 2026-03-26 12:53:15

6.9k

Views

Why does the Binomial Theorem use combinations and not permutations for its coefficients?

Published on 26 Mar 2026 - 12:53

score 4.1k · Answer 7 · 2019-02-21 13:33:40

4.1k

Views

Simple proof that $(1 + 1/n)^n$, $n \in \mathbb N$, is bounded above?

Published on 21 Feb 2019 - 13:33

score 289 · Answer 8 · 2019-02-27 07:08:20

289

Views

Prove that $16 ^ {2023} + 1$ is divisible by $17 ^ 2$.

Published on 27 Feb 2019 - 7:08

score 91 · Answer 9 · 2019-02-27 07:23:19

91

Views

Finding a sequence with some summation properties $\sum\binom{n}{k}a_k=\binom{2n}{n}$

Published on 27 Feb 2019 - 7:23

score 1.8k · Answer 10 · 2019-02-28 16:09:41

1.8k

Views

Maximum value of coefficient in Multinomial Expansion

Published on 28 Feb 2019 - 16:09

score 252 · Answer 11 · 2019-03-03 18:59:07

252

Views

For which $k$ the following equation has the greatest value: $ k \cdot\binom{99}{k} $?

Published on 03 Mar 2019 - 18:59

score 67 · Answer 12 · 2019-03-04 00:18:33

67

Views

How to evaluate a binomial sum with $2n$ in the exponent.

Published on 04 Mar 2019 - 0:18

score 79 · Answer 13 · 2019-03-06 05:03:52

79

Views

Showing an Inequality Holds True

Published on 06 Mar 2019 - 5:03

score 164 · Answer 14 · 2019-03-07 21:08:50

164

Views

$\int\frac{dx}{x(x+1)(x+2)\cdot\space...\space\cdot(x+n)}$

Published on 07 Mar 2019 - 21:08

score 87 · Answer 15 · 2019-03-10 16:01:54

87

Views

If $(1+x)^{n}=C_{0} + C_{1} x + C_{2} x^2+......C_{n} x^n$

Published on 10 Mar 2019 - 16:01

List Question

How can I prove $\frac {d}{dx} {x^n} = n x^{n-1}$ for $ n \in \Bbb R$ without circular reasoning?

How can I find the coefficient of $x^6$ in $(1+x+\frac{x^2}{2})^{10}$ efficiently with combinatorics?

Proving the connection between the Binomial Theorem and the product rule for derivatives

In the expansion of $a{x}^3 {(2+ax)}^{11}$ , the coefficient of the term in $x^5$ is $11880$. Find the value of $a$ .

Question related to Pascal Triangles and Counting Patterns

Why does the Binomial Theorem use combinations and not permutations for its coefficients?

Simple proof that $(1 + 1/n)^n$, $n \in \mathbb N$, is bounded above?

Prove that $16 ^ {2023} + 1$ is divisible by $17 ^ 2$.

Finding a sequence with some summation properties $\sum\binom{n}{k}a_k=\binom{2n}{n}$

Maximum value of coefficient in Multinomial Expansion

For which $k$ the following equation has the greatest value: $ k \cdot\binom{99}{k} $?

How to evaluate a binomial sum with $2n$ in the exponent.

Showing an Inequality Holds True

$\int\frac{dx}{x(x+1)(x+2)\cdot\space...\space\cdot(x+n)}$

If $(1+x)^{n}=C_{0} + C_{1} x + C_{2} x^2+......C_{n} x^n$

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