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 $S_\infty=\frac {a}{1-r}$

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: $S_\infty=\frac {50}{1-0.9}$

1-0.9=0.1 so you’ll end up with $S_\infty=\frac {50}{0.1}$

Then i will get $S\infty=500$

So now we know the approximate sum of the infinite geometric series 50, 45, 40.5, 36.45,… is 500.