Use the binomial theorem to prove the following: $$3 ^ { 100 } = \left( \begin{array} { c }
100 \
0
\end{array} \right) + \left( \begin{array} { c }
100 \
1
\end{array} \right) \cdot 2 + \left( \begin{array} { c }
100 \
2
\end{array} \right) \cdot 2 ^ { 2 } + \left( \begin{array} { c }
100 \
3
\end{array} \right) \cdot 2 ^ { 3 } + \cdots + \left( \begin{array} { c }
100 \
99
\end{array} \right) \cdot 2 ^ { 99 } + \left( \begin{array} { c }
100 \
100
\end{array} \right) \cdot 2 ^ { 100 }$$

Question

Use the binomial theorem to prove the following: $$3 ^ { 100 } = \left( \begin{array} { c } 
100 \
0
\end{array} \right) + \left( \begin{array} { c } 
100 \
1
\end{array} \right) \cdot 2 + \left( \begin{array} { c } 
100 \
2
\end{array} \right) \cdot 2 ^ { 2 } + \left( \begin{array} { c } 
100 \
3
\end{array} \right) \cdot 2 ^ { 3 } + \cdots + \left( \begin{array} { c } 
100 \
99
\end{array} \right) \cdot 2 ^ { 99 } + \left( \begin{array} { c } 
100 \
100
\end{array} \right) \cdot 2 ^ { 100 }$$

Quizplus · Accepted Answer

The Answer of Use the binomial theorem to prove the following: $$3 ^ { 100 } = \left( \begin{array} { c } 
100 \
0
\end{array} \right) + \left( \begin{array} { c } 
100 \
1
\end{array} \right) \cdot 2 + \left( \begin{array} { c } 
100 \
2
\end{array} \right) \cdot 2 ^ { 2 } + \left( \begin{array} { c } 
100 \
3
\end{array} \right) \cdot 2 ^ { 3 } + \cdots + \left( \begin{array} { c } 
100 \
99
\end{array} \right) \cdot 2 ^ { 99 } + \left( \begin{array} { c } 
100 \
100
\end{array} \right) \cdot 2 ^ { 100 }$$

Use the Binomial Theorem to Prove the Following