Use the Binomial Theorem to Prove the Following

question 144

Short Answer

Use the binomial theorem to prove the following: $\left( \begin{array} { l } 6 \\0\end{array} \right) + \left( \begin{array} { l } 6 \\1\end{array} \right) + \cdots + \left( \begin{array} { l } 6 \\6\end{array} \right) = 2 ^ { 6 } .$

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Definitions:

Biodiversity

The variety and variability of life on Earth, encompassing the diversity of species, genes, ecosystems, and ecological processes.

Biomass

The total mass of all living organisms in a specific area, habitat, or region.

Weirs

Low dams built across rivers to raise the level of water upstream or regulate its flow for purposes such as irrigation, fish trapping, and water diversion.

Fish Traps

Engineered structures placed in aquatic environments designed to trap fish or other aquatic animals.