This week we learned about infinite geometric series.
You can separate geometric series’ into two types, ones that diverge, and ones that converge.
If r > 1 or r < -1 then it diverges
If 0 < r < 1 or -1 < r < 0 then it converges
You can only find an approximate sum for infinite geometric series that converge, since the ones that diverge keep growing forever.
The formula for this is
I will use 50, 45, 40.5, 36.45,… as my example.
So far we know a=50 and r=0.9
Since r=0.9 we know it is converging and we can find an approximate sum.
If I plug what i know into the formula it will look like this:
1-0.9=0.1 so you’ll end up with
Then i will get
So now we know the approximate sum of the infinite geometric series 50, 45, 40.5, 36.45,… is 500.