Difference between r1.26 and the current
@@ -33,7 +33,7 @@
$(a+b)^2=1a^2+2ab+1b^2$$(a+b)^3=1a^3+3a^2b+3ab^2+1b^3$
$\vdots$
이런 수의 배열을 [[파스칼의_삼각형,Pascal_s_triangle]]이라고 한다.
이런 수의 배열을 [[파스칼_삼각형,Pascal_triangle]]이라고 한다.
----$(1+x)^n={}_n{\rm C}_0+{}_n{\rm C}_1x+{}_n{\rm C}_2x^2+\cdots+{}_n{\rm C}_nx^n$
에 $x=1$ 을 대입하면
@@ -68,21 +68,58 @@
$(a+b)^n=\sum_{r=0}^n \binom{n}{r} a^{n-r} b^r$(Jeffrey AEM 2001 p6)
----
For any positive integer $n,$
$(a+b)^n$
$=a^n$
$+na^{n-1}b$
$+\frac{n(n-1)}{1\cdot 2}a^{n-2}b^2$
$+\frac{n(n-1)(n-2)}{1\cdot2\cdot3}a^{n-3}b^3$
$+\cdots$
$+nab^{n-1}$
$+b^n$
For instance, // [[인수분해,factorization]] 중 일부
$(a+b)^2=a^2+2ab+b^2$
$(a-b)^2=a^2-2ab+b^2$
$(a+b)^3=a^3+3a^2b+3ab^2+b^3$
$(a-b)^3=a^3-3a^2b+3ab^2-b^3$
(Thomas 13e F-1 기본 공식과 법칙)
----
----
[[이항계수,binomial_coefficient]]
[[이항계수,binomial_coefficient]] ,,''n'',,C,,''k'',,
[[이항전개,binomial_expansion]][[이항분포,binomial_distribution]]
[[Date(2022-04-09T15:02:56)]]
[[이항급수,binomial_series]] - [[급수,series]] - writing
[[이항공식,binomial_formula]]
{
https://planetmath.org/BinomialFormula
[[공식,formula]]
}
[[이항항등식,binomial_identity]] - [[항등식,identity]]
{
https://mathworld.wolfram.com/BinomialIdentity.html
}
----
WpKo:이항_정리
Twins:
[[WpKo:이항_정리]]
https://everything2.com/title/Binomial+Theorem
https://ghebook.blogspot.com/2010/10/binomial-theorem.html
https://artofproblemsolving.com/wiki/index.php/Binomial_Theorem
[[Date(2022-04-09T04:13:45)]]
https://mathworld.wolfram.com/BinomialTheorem.html
https://ncatlab.org/nlab/show/binomial+theorem
https://planetmath.org/binomialtheorem
https://proofwiki.org/wiki/Binomial_Theorem
(semi-twin: binomial_series - [[급수,series]] 관점 => https://mathworld.wolfram.com/BinomialSeries.html ... Google:binomial.series )
----
Up: [[정리,theorem]]
친숙한 알파벳으로 다시 쓰면,
복소수에도 성립
for
이항계수는 CHK k는 뭐지? 책이 잘못?
이항계수는 CHK k는 뭐지? 책이 잘못?
nCr=nCn-r이므로 대칭형이다.
에 을 대입하면
임을 알 수 있다.
from hightop; chk
and
Binomial theorem when is a positive integer
가 실수이고 이 양의 정수이면
이항계수,binomial_coefficient
를 쓰면
(Jeffrey AEM 2001 p6)
가 실수이고 이 양의 정수이면
2022-04-10
이항급수,binomial_series - 급수,series - writing
이항공식,binomial_formula
{
https://planetmath.org/BinomialFormula
공식,formula
}
이항항등식,binomial_identity - 항등식,identity
{
https://mathworld.wolfram.com/BinomialIdentity.html
}
이항급수,binomial_series - 급수,series - writing
이항공식,binomial_formula
{
https://planetmath.org/BinomialFormula
공식,formula
}
이항항등식,binomial_identity - 항등식,identity
{
https://mathworld.wolfram.com/BinomialIdentity.html
}
Twins:
이항_정리
https://everything2.com/title/Binomial Theorem
https://ghebook.blogspot.com/2010/10/binomial-theorem.html
https://artofproblemsolving.com/wiki/index.php/Binomial_Theorem
이항_정리
https://everything2.com/title/Binomial Theorem
https://ghebook.blogspot.com/2010/10/binomial-theorem.html
https://artofproblemsolving.com/wiki/index.php/Binomial_Theorem
2022-04-09
https://mathworld.wolfram.com/BinomialTheorem.html
https://ncatlab.org/nlab/show/binomial theorem
https://planetmath.org/binomialtheorem
https://proofwiki.org/wiki/Binomial_Theorem
(semi-twin: binomial_series - 급수,series 관점 => https://mathworld.wolfram.com/BinomialSeries.html ... binomial.series )
https://mathworld.wolfram.com/BinomialTheorem.html
https://ncatlab.org/nlab/show/binomial theorem
https://planetmath.org/binomialtheorem
https://proofwiki.org/wiki/Binomial_Theorem
(semi-twin: binomial_series - 급수,series 관점 => https://mathworld.wolfram.com/BinomialSeries.html ... binomial.series )
Up: 정리,theorem