Use the Binomial Theorem to Prove the Following

question 121

Short Answer

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

---

Definitions:

Bile

Bile is a digestive fluid produced by the liver and stored in the gallbladder, aiding in the digestion and absorption of fats in the small intestine.

Vitamins

Organic compounds that are essential for normal growth and nutrition and are required in small quantities in the diet because they cannot be synthesized by the body.

Minerals

Inorganic nutrients ingested as salts dissolved in food and water.

Free-Living Flatworms

Flatworms that are not parasitic and live independently in various aquatic or moist terrestrial environments.