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# cool question

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You have a whole pizza in the refrigerator. On your first trip to the refrigerator, you eat half the pizza. On each successive trip, you eat half of the remaining pizza. After five trips to the refrigerator, what fractional part of the pizza have you eaten?

Dec 27, 2018

#1
+4569
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This is just a geometric series, so the answer is:

\begin{align*} \frac12+\frac1{2^2}+\frac1{2^3}+\frac1{2^4}+\frac1{2^5} &= \frac{\frac12\left(1-\left(\frac12\right)^5\right)}{1-\frac12}\\ &=1-\left(\frac12\right)^5\\ &=1-\frac1{32}\\ &=\boxed{\frac{31}{32}}. \end{align*}

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Dec 27, 2018
#2
+111328
+2

This is given by  the sum of a geometric series

sum  =  first term ( 1 - geometric ratio^n) / ( 1 - geometric ratio )

Where

first term = 1/2

n = 5

geometric ratio = 1/2

So...

(1/2)  ( 1 - (1/2)^5) / (1 - 1/2)    = 31 / 32  of the pizza

Dec 27, 2018