the_binomial_theorem
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the_binomial_theorem [2020/11/04 16:02] – [계수] hkimscil | the_binomial_theorem [2020/11/18 00:14] – [계수] hkimscil | ||
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&{3 \choose 0}\; {3 \choose 1}\; {3 \choose 2}\; {3 \choose 3}& \\ | &{3 \choose 0}\; {3 \choose 1}\; {3 \choose 2}\; {3 \choose 3}& \\ | ||
&{4 \choose 0}\; {4 \choose 1}\; {4 \choose 2}\; {4 \choose 3}\; {4 \choose 4}& \\ | &{4 \choose 0}\; {4 \choose 1}\; {4 \choose 2}\; {4 \choose 3}\; {4 \choose 4}& \\ | ||
+ | &{5 \choose 0}\; {5 \choose 1}\; {5 \choose 2}\; {5 \choose 3}\; {5 \choose 4}\; {5 \choose 5} & \\ | ||
\end{eqnarray*} | \end{eqnarray*} | ||
\begin{eqnarray*} | \begin{eqnarray*} | ||
- | & | + | & {\large |
- | & 1 1 & \\ | + | & {\large |
- | & 1 2 1 & \\ | + | & {\large |
- | & 1 3 3 1 & \\ | + | & {\large |
- | & 1 4 6 4 1 & \\ | + | & {\large |
+ | & {\large 1\quad 5\quad 10\quad 10\quad 5\quad | ||
\end{eqnarray*} | \end{eqnarray*} | ||
Line 98: | Line 100: | ||
\end{eqnarray*} | \end{eqnarray*} | ||
+ | 예를 들면, 아래와 같다. ($n = 3$ 인경우) | ||
\begin{eqnarray*} | \begin{eqnarray*} | ||
- | (a + b)^{3} = & \sum^{3}_{k=0}{{3}\choose{k}} a^{3-k} b^{k} \\ | + | (a + b)^{3} |
& = & {{3}\choose{0}} a^{3-0} b^{0} + {{3}\choose{1}} a^{3-1} b^{1} + {{3}\choose{2}} a^{3-2} b^{2} + {{3}\choose{3}} a^{3-3} b^{3} \\ | & = & {{3}\choose{0}} a^{3-0} b^{0} + {{3}\choose{1}} a^{3-1} b^{1} + {{3}\choose{2}} a^{3-2} b^{2} + {{3}\choose{3}} a^{3-3} b^{3} \\ | ||
& = & 1 \cdot a^{3} b^{0} + 3 \cdot a^{2} b^{1} + 3 \cdot a^{1} b^{2} + 1 \cdot a^{0} b^{3} \\ | & = & 1 \cdot a^{3} b^{0} + 3 \cdot a^{2} b^{1} + 3 \cdot a^{1} b^{2} + 1 \cdot a^{0} b^{3} \\ |
the_binomial_theorem.txt · Last modified: 2020/11/18 00:20 by hkimscil