Question 1054149
<font color=black size=3>This is a <a href = "http://mathworld.wolfram.com/GeometricSeries.html">geometric series</a>. In this case, 


first term = a = 1
common ratio = r = 1/2 = 0.5


In plain english, we start with the term 1. To get the next term, we multiply 1 by 1/2 to get 1/2. So the second term is 1/2. The third term is 1/4 since (second term)*(r) = (1/2)(1/2) = 1/4. And so on. This is continued on forever to generate an infinite number of terms. These terms are added up.


The question is: do all of the terms add up to a fixed number? Or do these terms just go on forever making the sum larger and larger? 


Since r = 1/2, which is between -1 and +1, this means that the series does converge. The sum slowly gets closer and closer to a fixed value. The sum does NOT go on forever.


Let's find that infinite sum S


{{{S = a/(1-r)}}}


{{{S = 1/(1-0.5)}}} Plug in a = 1 and r = 0.5 (same as 1/2)


{{{S = 1/(0.5)}}}


{{{S = 2}}}


So this means 
1+1/2+1/4... = 2</font>