Finding the infinite sum of geometric series is quite simple. Simply applying the formula will get the answer. Remember that this will only work for geometric series not arithmetic series.

This will only work if the infinite sum of a geometric series if r < 1
The formula for finding the infinite sum of a geometric series is:
S= ((t1) / (1-r))
To find where an infinite geometric converges, set r < 1 and solve for the x term
this how you are to write a repeating decimal as a fraction. To do this follow this formula: (what’s repeating / place-1)

Ex 1: Find the sum of the infinite geometric series: -3, 12, -36, 144...
• S=t1 / 1-r = -3 / 1- (-4)
• S=24 / 5
-Sameer