This week we learned about diverging and converging series and if we can find the sum of an infinite geometric series. When we learned about diverging series, we used desmos, and were shown that if you have a series and the difference is r>1 then the number will keep getting larger and larger. And if the difference is r<-1, than the numbers will get bigger and bigger but will alternate between positive and negative numbers, making the graph on desmos go in a zig zag pattern. For both of these types of series, which are diverging, you cannot find the sum of the series because the numbers are constantly getting higher and never stop.

When we learned about converging series, we were shown in desmos that in a series, if the difference is 0<r<1 then the numbers in the series will get smaller and smaller, getting closer to zero but never actually getting to it, because you can always add more decimal places. And if the difference is -1<r<0, then the numbers will get smaller and smaller and alternate between positive and negative, again making a zig zag pattern on desmos.

However, with converging series you can find the sum if the infinite series by using the formula S_{00} = \frac{a}{1-r}. The picture below is an example of how to use this formula to find the infinite sum of a series.