+0

# Help

+1
30
2
+312

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
+114096
+2

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

Jan 5, 2021
#2
+312
+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