Question

What is the sum of the infinite geometric series? mc010-1.jpg

Answer 1

You haven't provided the series, therefore, I can only help with the concept.

For an infinite geometric series, we have two possibilities for the common ratio (r):
for r > 1, the terms in the series will keep increasing infinitely and the only possible logic summation of the series would be infinity
for r < 1, the terms will decrease, therefore, we can formulate a rule to get the sum of the infinite series

In an infinite series with r < 1, the summation can be found using the following rule:
sum = $\frac{a_{1} }{1-r}$
where:
a₁ is the first term in the series
r is the common ratio

Example:
For the series:
2 , 1, 0.5 , 0.25 , ....
we have:
a₁ = 2
r = 0.5
Therefre:
sum = $\frac{2}{1-0.5} = 4$

Hope this helps :)