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Equation Rather than to Calculate it Manually

One day your economics professor shows you a picture of a BMW automobile. You mess around with different configurations for the available options and accesories and it can be yours for $77,942. You notice a rather sinister glint in your professor's eye as he notes your interest in the car, but tells you nonetheless that you won't have to actually torpedo your college fund to make your dreams come true. Instead, he would be willing to front you the money if you would be willing to front you the money if you would only agree to fulfill the following terms before you graduate: Bring him a chessboard and place one penny on the first square, two on the second, four on the third, and so forth, doubling the number of pennies at every stage, until whole board is filled up. That's it! YOur material dreams for pennies? Would you accept this deal and why? (Min. requirement: calculate the pecuniary amount on the very last square of the chessboard).

I calculated manually 8 rows, 8 columns x double.The answer 9,223,372,036,86 E18 I want to know if there's an equation that could make it easier to calculate.

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Pennies on square 1 = 1 = 20
Pennies on square 2 = 2 = 21
Pennies on ...

Solution Summary

The equations rather than calculating manuals are determined.