In this week’s Math 11 Pre-Cal I learned that you can actually determine the exact Sum of Infinite Geometric Series in certain situations, when they are converges.( when -1<r<1) as with a rate less than 1 and greater than -1 the next term will get closer and closer to zero, therefore there is a determinable sum. In the case of a diverging series, the sum will get infinity big and therefor we can’t determine the exact sum.
The equation for the sum of an regular Geometric Series is
When -1<r<1 approaches 0 as n increases indefinitely.
So, Sn approaches Sn= , therefor
A Infinite Geometric Series where r=0.5