Use the binomial theorem to prove the following: $$\left( \begin{array} { c }
100 \
0
\end{array} \right) + \left( \begin{array} { c }
100 \
2
\end{array} \right) + \left( \begin{array} { c }
100 \
4
\end{array} \right) + \left( \begin{array} { c }
100 \
6
\end{array} \right) + \cdots + \left( \begin{array} { c }
100 \
98
\end{array} \right) + \left( \begin{array} { c }
100 \
100
\end{array} \right) = \left( \begin{array} { c }
100 \
1
\end{array} \right) + \left( \begin{array} { c }
100 \
3
\end{array} \right) + \left( \begin{array} { c }
100 \
5
\end{array} \right) + \cdots + \left( \begin{array} { c }
100 \
97
\end{array} \right) + \left( \begin{array} { c }
100 \
99
\end{array} \right) \text {. }$$

Question

Use the binomial theorem to prove the following: $$\left( \begin{array} { c } 
100 \
0
\end{array} \right) + \left( \begin{array} { c } 
100 \
2
\end{array} \right) + \left( \begin{array} { c } 
100 \
4
\end{array} \right) + \left( \begin{array} { c } 
100 \
6
\end{array} \right) + \cdots + \left( \begin{array} { c } 
100 \
98
\end{array} \right) + \left( \begin{array} { c } 
100 \
100
\end{array} \right) = \left( \begin{array} { c } 
100 \
1
\end{array} \right) + \left( \begin{array} { c } 
100 \
3
\end{array} \right) + \left( \begin{array} { c } 
100 \
5
\end{array} \right) + \cdots + \left( \begin{array} { c } 
100 \
97
\end{array} \right) + \left( \begin{array} { c } 
100 \
99
\end{array} \right) \text {. }$$

Quizplus · Accepted Answer

The Answer of Use the binomial theorem to prove the following: $$\left( \begin{array} { c } 
100 \
0
\end{array} \right) + \left( \begin{array} { c } 
100 \
2
\end{array} \right) + \left( \begin{array} { c } 
100 \
4
\end{array} \right) + \left( \begin{array} { c } 
100 \
6
\end{array} \right) + \cdots + \left( \begin{array} { c } 
100 \
98
\end{array} \right) + \left( \begin{array} { c } 
100 \
100
\end{array} \right) = \left( \begin{array} { c } 
100 \
1
\end{array} \right) + \left( \begin{array} { c } 
100 \
3
\end{array} \right) + \left( \begin{array} { c } 
100 \
5
\end{array} \right) + \cdots + \left( \begin{array} { c } 
100 \
97
\end{array} \right) + \left( \begin{array} { c } 
100 \
99
\end{array} \right) \text {. }$$

Use the Binomial Theorem to Prove the Following