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Newton's binomial theorem with induction

score 374 · Answer 1 · 2015-10-04 09:15:52

374

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Newton's binomial theorem with induction

Published on 04 Oct 2015 - 9:15

score 551 · Answer 2 · 2026-03-27 14:10:39

551

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Calculating last digit of a number using binomial theorem

Published on 27 Mar 2026 - 14:10

score 1.9k · Answer 3 · 2015-10-06 19:07:13

1.9k

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Expansion of $\frac{1}{\sqrt{1-4x}}$

Published on 06 Oct 2015 - 19:07

score 271 · Answer 4 · 2015-10-07 17:19:39

271

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Prove that $2^{n-1}$ divides $\binom{n}{1} + \binom{n}{3}5 + \binom{n}{5}25 + \binom{n}{7}125 + \cdots$ for $n \geqslant 1$.

Published on 07 Oct 2015 - 17:19

score 49 · Answer 5 · 2015-10-10 10:01:47

49

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$\binom{n}{0}-\frac{1}{(2+\sqrt3)^2}\binom{n}{2}+\frac{1}{(2+\sqrt3)^4}\binom{n}{4}-\frac{1}{(2+\sqrt3)^6}\binom{n}{6}+.....=$

Published on 10 Oct 2015 - 10:01

score 56 · Answer 6 · 2026-04-01 12:41:21

56

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Show that the interest rate sequence is Cauchy

Published on 01 Apr 2026 - 12:41

score 41 · Answer 7 · 2015-10-18 06:16:06

41

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Binomial theorem to find coeff of $x^n$

Published on 18 Oct 2015 - 6:16

score 102 · Answer 8 · 2026-02-28 03:01:28

102

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How to prove that $\sum_{i=0}^n\frac{(a;q)_i}{(q;q)_i}\frac{(b;q)_{n-i}}{(q;q)_{n-i}}a^{n-i}=\frac{(ab;q)_n}{(q;q)_n}$?

Published on 28 Feb 2026 - 3:01

score 81 · Answer 9 · 2026-03-18 23:52:52

81

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Is a binomial expansion of the denominator valid here?

Published on 18 Mar 2026 - 23:52

score 337 · Answer 10 · 2026-03-18 23:46:56

337

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approximate $\sum_{k=0}^n {n \choose k} k! n^{-k} \sim {\sqrt{\pi n}\over \sqrt{2}}$

Published on 18 Mar 2026 - 23:46

score 158 · Answer 11 · 2026-03-21 12:49:18

158

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On the binomial series $(1+\frac{1}{8n})^{1/2}$, where $n$ is an even perfect number

Published on 21 Mar 2026 - 12:49

score 722 · Answer 12 · 2015-10-24 12:38:59

722

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Prove that sum $(\sqrt2+1)^n+(\sqrt2-1)^n$ is rational for even numbers

Published on 24 Oct 2015 - 12:38

score 130 · Answer 13 · 2026-03-06 07:35:43

130

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Prove: ${n\choose 1}-3{n\choose 3}+9{n\choose 5}-...=\frac{-1}{\sqrt{3}}(-2)^n\sin\frac{2n\pi}{3}$

Published on 06 Mar 2026 - 7:35

score 113 · Answer 14 · 2026-03-14 03:09:10

113

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Proving a binomial identity

Published on 14 Mar 2026 - 3:09

score 384 · Answer 15 · 2026-03-06 02:59:08

384

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Binomial theorem and it's geometric interpretation with functions

Published on 06 Mar 2026 - 2:59

List Question

Newton's binomial theorem with induction

Calculating last digit of a number using binomial theorem

Expansion of $\frac{1}{\sqrt{1-4x}}$

Prove that $2^{n-1}$ divides $\binom{n}{1} + \binom{n}{3}5 + \binom{n}{5}25 + \binom{n}{7}125 + \cdots$ for $n \geqslant 1$.

$\binom{n}{0}-\frac{1}{(2+\sqrt3)^2}\binom{n}{2}+\frac{1}{(2+\sqrt3)^4}\binom{n}{4}-\frac{1}{(2+\sqrt3)^6}\binom{n}{6}+.....=$

Show that the interest rate sequence is Cauchy

Binomial theorem to find coeff of $x^n$

How to prove that $\sum_{i=0}^n\frac{(a;q)_i}{(q;q)_i}\frac{(b;q)_{n-i}}{(q;q)_{n-i}}a^{n-i}=\frac{(ab;q)_n}{(q;q)_n}$?

Is a binomial expansion of the denominator valid here?

approximate $\sum_{k=0}^n {n \choose k} k! n^{-k} \sim {\sqrt{\pi n}\over \sqrt{2}}$

On the binomial series $(1+\frac{1}{8n})^{1/2}$, where $n$ is an even perfect number

Prove that sum $(\sqrt2+1)^n+(\sqrt2-1)^n$ is rational for even numbers

Prove: ${n\choose 1}-3{n\choose 3}+9{n\choose 5}-...=\frac{-1}{\sqrt{3}}(-2)^n\sin\frac{2n\pi}{3}$

Proving a binomial identity

Binomial theorem and it's geometric interpretation with functions

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