Question

(1/256)^-1 16/(8)^-1 evaluate


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Answer 1

Answer:

In mathematics, the infinite series

1

/

4

+

1

/

16

+

1

/

64

+

1

/

256

+ ⋯ is an example of one of the first infinite series to be summed in the history of mathematics; it was used by Archimedes circa 250–200 BC.[1] As it is a geometric series with first term

1

/

4

and common ratio

1

/

4

, its sum is

{\displaystyle \sum _{n=1}^{\infty }{\frac {1}{4^{n}}}={\frac {\frac {1}{4}}{1-{\frac {1}{4}}}}={\frac {1}{3}}.}{\displaystyle \sum _{n=1}^{\infty }{\frac {1}{4^{n}}}={\frac {\frac {1}{4}}{1-{\frac {1}{4}}}}={\frac {1}{3}}.}