In this unit we learned how to find the infinite sum of a geometric series.

To find the infinite sum of a geometric series we need to first find out the common ratio to see if the series converges. Only converging series can have a finite infinite sum.

To find the common ratio we use this formula:

Next we plug in the appropriate numbers into the formula and solve for the answer. t₁=-10 & t₂=-20/3

As we can see -1<r<1 and r does not equal 0, so we know that the geometric series is converging.

Since a=the first term and we know a=10, we can plug that information into the infinite geometric series formula

to find the infinite sum:

From what you can see above, the infinite sum is 6.

The infinite sum works for converging geometric series because when you add up infinite terms of a converging geometric series, it will add up to a certain number.