Question

If we are not allowed to put zero at the starting of binomial expansion, then why are we able to put it later, when it is solved?

score 282 · Answer 1 · 2021-10-09 09:13:15

282

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If we are not allowed to put zero at the starting of binomial expansion, then why are we able to put it later, when it is solved?

Published on 09 Oct 2021 - 9:13

score 601 · Answer 2 · 2021-10-10 15:44:16

601

Views

Expressing the binomial coefficients in terms of factorials and simplify

Published on 10 Oct 2021 - 15:44

score 172 · Answer 3 · 2026-03-28 11:22:03

172

Views

I have a question about combination series. i don't understand that

Published on 28 Mar 2026 - 11:22

score 116 · Answer 4 · 2021-10-12 08:09:45

116

Views

Proof for the given identity of $\frac{1}{1-az-bz^2}$

Published on 12 Oct 2021 - 8:09

score 132 · Answer 5 · 2026-02-23 15:11:06

132

Views

Prove using binomial expansion that $\sum _{k=0}^n\:k\:\begin{pmatrix}n\\ k\end{pmatrix}=n\:2\:^{n-1},\:\forall \:n\in \mathbb{Z},\:n\ge 1$

Published on 23 Feb 2026 - 15:11

score 57 · Answer 6 · 2021-10-15 10:38:22

57

Views

Find the value of $\underset{0\leq i \lt j\leq n}\sum{\binom{n}{i}}$

Published on 15 Oct 2021 - 10:38

score 172 · Answer 7 · 2026-04-04 02:33:48

172

Views

What is the sum of a binomial series where the bionomials terms are raised to a power?: $ \sum\limits_{k=0}^\infty \binom{n}{k}^dx^k$

Published on 04 Apr 2026 - 2:33

score 101 · Answer 8 · 2026-03-29 05:06:28

101

Views

If $\{x\}$ denotes the fractional part of x, then what is $\{\dfrac{3^{2n}}{8}\}$, where n $\in$ N

Published on 29 Mar 2026 - 5:06

score 44 · Answer 9 · 2021-10-17 09:34:44

44

Views

Value of $\ \sum_{r=1}^{n} (-1)^{r-1}(1+ \dfrac{1}{2} + \dfrac{1}{3} + \ ...\ +\dfrac{1}{r}) {n \choose r}$

Published on 17 Oct 2021 - 9:34

score 220 · Answer 10 · 2026-04-05 22:33:14

220

Views

converting binomial product to a sum

Published on 05 Apr 2026 - 22:33

score 199 · Answer 11 · 2021-10-22 17:51:05

199

Views

Binomial Expansion with Derivatives

Published on 22 Oct 2021 - 17:51

score 389 · Answer 12 · 2021-10-23 21:01:49

389

Views

Drawing black and white balls

Published on 23 Oct 2021 - 21:01

score 325 · Answer 13 · 2021-10-24 09:32:23

325

Views

Bernoulli inequality using binomial theorem

Published on 24 Oct 2021 - 9:32

score 1.1k · Answer 14 · 2021-10-26 09:33:52

1.1k

Views

Quickly simplify $(\sqrt{3}+1)^6+(\sqrt{3}-1)^6$

Published on 26 Oct 2021 - 9:33

score 178 · Answer 15 · 2026-04-01 02:50:19

178

Views

$p(q(t)) \neq q(p(t))$ for every $t$, find all degrees of monic polynomials

Published on 01 Apr 2026 - 2:50

List Question

If we are not allowed to put zero at the starting of binomial expansion, then why are we able to put it later, when it is solved?

Expressing the binomial coefficients in terms of factorials and simplify

I have a question about combination series. i don't understand that

Proof for the given identity of $\frac{1}{1-az-bz^2}$

Prove using binomial expansion that $\sum _{k=0}^n\:k\:\begin{pmatrix}n\\ k\end{pmatrix}=n\:2\:^{n-1},\:\forall \:n\in \mathbb{Z},\:n\ge 1$

Find the value of $\underset{0\leq i \lt j\leq n}\sum{\binom{n}{i}}$

What is the sum of a binomial series where the bionomials terms are raised to a power?: $ \sum\limits_{k=0}^\infty \binom{n}{k}^dx^k$

If $\{x\}$ denotes the fractional part of x, then what is $\{\dfrac{3^{2n}}{8}\}$, where n $\in$ N

Value of $\ \sum_{r=1}^{n} (-1)^{r-1}(1+ \dfrac{1}{2} + \dfrac{1}{3} + \ ...\ +\dfrac{1}{r}) {n \choose r}$

converting binomial product to a sum

Binomial Expansion with Derivatives

Drawing black and white balls

Bernoulli inequality using binomial theorem

Quickly simplify $(\sqrt{3}+1)^6+(\sqrt{3}-1)^6$

$p(q(t)) \neq q(p(t))$ for every $t$, find all degrees of monic polynomials

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