[math] \displaystyle
\left ( a+b \right )^n \\
= \binom{n}{0}a^nb^0 + \binom{n}{1}a^{n-1}b^1 + \binom{n}{2}a^{n-2}b^2 + \cdots \\
+ \binom{n}{n-2}a^2b^{n-2} + \binom{n}{n-1}a^1b^{n-1} + \binom{n}{n}a^0b^n \\
= \sum_{i=0}^n \binom{n}{i}a^{n-i}b^i \\
\binom{n}{r} = \dfrac{n!}{r!~(n-r)!} = ~_nC_r
[/math]
Can anyone explain to a brainlet how to find the coefficient of some term when some expression is expanded (see...
Brayden King
Matthew Lee
[math] \displaystyle
\left ( a+b \right )^n \\
= \binom{n}{0}a^nb^0 + \binom{n}{1}a^{n-1}b^1 + \binom{n}{2}a^{n-2}b^2 + \cdots \\
+ \binom{n}{n-2}a^2b^{n-2} + \binom{n}{n-1}a^1b^{n-1} + \binom{n}{n}a^0b^n \\
\displaystyle
= \sum_{i=0}^n \binom{n}{i}a^{n-i}b^i \\
\binom{n}{r} = \dfrac{n!}{r!~(n-r)!} = ~_nC_r
[/math]
Sebastian Jones
[math] \displaystyle
\left ( a+b \right )^n \\
= \binom{n}{0}a^nb^0 + \binom{n}{1}a^{n-1}b^1 + \binom{n}{2}a^{n-2}b^2 + \cdots \\
+ \binom{n}{n-2}a^2b^{n-2} + \binom{n}{n-1}a^1b^{n-1} + \binom{n}{n}a^0b^n \\
\displaystyle
= \sum_{i=0}^n \binom{n}{i}a^{n-i}b^i \\
\displaystyle
\binom{n}{r} = \dfrac{n!}{r!~(n-r)!} = ~_nC_r
[/math]