Express the Following Sum in Closed Form (Without Using a Summation

question 16

Essay

Express the following sum in closed form (without using a summation symbol and without using an ellipsis . . . ): $\sum _ { k = 0 } ^ { n } \left( \begin{array} { l } n \\k\end{array} \right) 7 ^ { k }$

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Definitions:

Mesozoic Era

A major subdivision of geologic time from 251 million years ago (Ma) to 65 Ma; characterized by dinosaurs.

Jurassic Period

A geologic period and system that occurred about 201 to 145 million years ago, known for the prevalence of dinosaurs and the breakup of the supercontinent Pangea.

Numeric Age

Geologic age of a rock, sediment, fossil, or event calculated in thousands, millions, or billions of years before present; synonym: absolute age.

Actual Age

The precise age or date of an object or event, usually determined through radiometric dating or other scientific methods.