+0  
 
+1
92
2
avatar+303 

Find the sum of the first six terms in the geometric sequence \(\frac12,\frac14,\frac18,\dots\). Express your answer as a common fraction.

 Jan 5, 2021
 #1
avatar+117576 
+2

S = (1/2) ( 1 - (1/2)^6 )  / ( 1 - 1/2)    =  63/64     ( we could see this from the other problem )

 

cool cool cool

 Jan 5, 2021
 #2
avatar+303 
+1

This 6-term geometric series has first term \(a_0 = \frac12\) and ratio 1/2, so it has value

\(\begin{align*} \frac{\frac12(1-\left(\frac12\right)^{6})}{1-\frac12} &= 1-\left(\frac12\right)^{6}\\ &= 1-\frac1{64}\\ &= \boxed{\frac{63}{64}}. \end{align*}\)

 Jan 5, 2021

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